Well, your religion isn't going to be much help stemming the tide. The cheap/powerful prophets still require significant faith generation, and your earlier screenshot had you at about 22 fpt, which is not nearly enough to combat this religious tide. From a religion standpoint, you got hit by a bus, and your best plan will be to generate as much faith as possible to spawn inquisitors and GPrs to keep you cities in good shape.
Assuming, that is, that Christianity's pantheon and follower beliefs are inferior to yours. What beliefs did the Celts select? You might be well off throwing in the religion towel and focusing on conventional war.
On plunging happiness, if the AI is going to bust your lux trades, and your religion is at risk, you're going to have to look to mercantile CSs (and other CSs that have a unique lux for you). Also, as you take cities, raze or sell everything except the capitals, no matter how superficially appealing the city may seem ("Gee, it has a university, workshop, extra citrus and 3 coal. Maybe I should ke..." NO!). Unless it is a capital or has a particularly useful wonder, raze it or sell it. Domination victory is all about taking capitals, not taking cities to round out your empire.
EDIT: Also, keep in mind that a city's population is cut in half every time it is taken. For larger cities that you've decided not to keep, where the raze time can be 8-10-12 turns after conquest, take the city, set it to raze, and then withdraw the unit occupying the city. The AI may try to retake the city, which is OK. Population cut in half again. Then retake the city--pop cut in half again. Then let the final raze happen. Much lower unhappiness and shorter raze time.