I think it may be best to split this into two questions..or maybe three...how to win a culture victory? how to win your current game? and maybe ..is a CV possibly in your game? I'm not sure as we really have little info about it. I can only surmise that you've likely advanced at least close to mid-game.
So, I will try to give some general pointers on CV, but there's really not much advice I can give specifically toward your game without seeing a save or some screenshots, both of which are the basic protocol on this forum.
First, CV is probably the one VC that one generally goes for and plans from the start..for optimal play..as an optimal CV game requires planning from the start - it is the most unique of Victory Conditions(VC). Yeah, it's possible to direct your game to towards CV later in the game, but for pure fast CVs you plan for the start.
As with other general advice, it is still recommended to ignore the early religions, and basically start your game as you would any other ...worker first and worker techs (food/production). However, religions are certainly important so you want to open the doors to your zealous neighbors so the spread them. More religions the better. Later you may certainly shoot for religions from CoL and Paci if you like - and these are important techs for CV anyway.
So, the keys to CV, assuming normal settings:
1) not absolutely necessary, but usually try for at least 9 cities..if some early warring is in the cards, then a capture capital or two is nice as these can often make good legendary (L) cities, whether cottages or gp farms
2) L cities are usually a strong cottaged bureau cap, and either secondary cottaged cities or food cities that can build some wonders. Wonders are not integral to CV games other than a couple of key ones, and you don't want to mix your GP pool to much as you mainly want to produce Great Artists, and many of them
3) All other cities besides the 3 L cities are disposable. What I mean by this is you either abuse them for production of temples, missionaries, or you grow them to run artists specialists. In fact, it is highly advisable to overlap some helper cities with any cottage cities like your capital to help grow cottages early with tile sharing
4) You can shoot for the early Great Scientist for an academy in your cap and maybe one or two more for some key bulbs to Liberalism, but otherwise you want great artists...many of them...an odd great person is ok as you can use it for a well timed Golden Age which not only helps in culture production, but in producing more Great Artists
5) Build culture multiplier buildings. This is where religion really comes into play. Each religion's "cathedral" type build provides a 50% bonus on culture in that city. Later the Hermitage from "Nationalism" ..a key tech and likely the one you Lib, can be built in capital. (note: you may start to see that marble is a very nice resource for CV as I believe all artists producing wonders and some culture buildings get a bonus from it. Some of the religious buildings get bonus from stone or copper.
6) Generally your cottaged capital is your "measuring stick" for CV timing if this is the route you chose. Each should be heavily cottaged with lots of rivers - flood plains even better. Get culture multipliers in there as fast as you can and Hermitage, even whip when it is reasonable to do so, while helper cities keep those cottages working. Once you reach the point where it is time to turn culture slider to 100% and multipliers in place, use that city to gauge the timing of when it will get L. Meanwhile, great artists production should already be in full force. Do not build great works immediately, but rather hold all your great artists until you can mathematically calculate which cities to bomb with great works such that the timing of the 3 L cities should be very close together.
7) Tech priorities - depends on level since in on higher levels you might be trading for certain techs, but on Monarch level with good play there should be no reason you cannot win the race to these techs. You can Oracle something like Code of Laws, or even go for Civil Service, but is not necessary and Oracle pollutes your gene pool. Mids is nice for early representation, but is a lot of hammers to invest. Later happiness will not be an issue anyway.
-techs: Code of Laws > Civil Service / Aesths>Lit>Drama>Music (keep free Great Artist / Paci>Paper>Edu>Lib>Nationalism
-the last tech you would like to have is Printing Press for cottage boost, and after it is time to shut down research for culture
8) You will want to be in Bureaucracy as soon as possible for boost commerce/hammers in cap to research fast and get building up fast. But your final target for civics is:
HR or Representation (does not really matter, and most likely you would be in HR at some point early on unless you built Mids)
Free Speech
Caste System
Mercantilism is okay, but not essential - otherwise you may still be in the default civic
Pacifism (OR likely early on for building production)
obviously, you have ideally been running a religion that should not put you in too much danger, and since you have spread all your religions everywhere it should not matter..so do what is best for diplo
9) Speaking of diplo..this is key for CV as generally it is a peaceful game. So keep up relations as best as possible with everyone. Psychos - you may want to kill them early on to avoid the later hassle or work towards Friendship and just bribe them into wars to keep them off your back. You might fight early as I mentioned, but otherwise you don't want much of a standing army in order to keep maintenance low.
10) Wonders: Parthenon, Mauso, Sistine Chapel (most important really), Taj Mahal (if possible time completion to when you go max culture...harder to do the higher the level and/or without marble)
- the above are all very helpful, but Statue of Zeus (ivory) and Notre Dame(stone) are okay too simply for culture and artists points..but don't waste time on them if they are a distraction or you don't have the resource
National Wonders: National Epic and Hermitage are really the only key ones..everything else is not essential at all and just pollutes anyway
Alternate approach: Basically eschew cottages for food and production and more focused great artist production and bombing. Maybe build more wonders in the L cities regardless, especially if Industrious and have stone/marble. Sistine Chapel is key wonder here without question as you will get a lot of culture from the artists you run. This often the best approach on certain maps like watery maps with less cottage potential anyway. Philosophical leaders are great.
Speaking of which Spiritual, Financial, Philosophical and Industrious are best traits for CV, especially in combination (there is no Philo/IND leader)
Lastly, if you are starting down the path of CV quite late game, your best approach may be to combine as much of the above advice with Corporations that produce culture and food.
edit: oh ..and gold is important. You want to be keeping your culture slider at 100% as much as possible. Make sure you are always trading extra resources for gold per turn, and note that happy resource become irrelevant once you do run the culture slider, but your health resource will probably be needed, so only trade extras.
And trade tech for gold as much as you can. Sometimes AIs will get large chunks of gold from fail wonders or otherwise, so keep an eye for that. Trading techs should keep diplo high as well, and lead to additional diplo bonus. Just be wary of the diplo landscape and Worst Enemies, but otherwise trade techs liberally once research is shut off.
small and compact overlapped empire helps cut maintenance cost too, but you will still need as much gold as you can nab from others