Specific levels of unhappiness are less relevant than relative levels of ideological influence/pressure. On the third tab of the Culture Overview, where it shows whether civs are content, or have dissidents, or experiencing a revolutionary wave, etc., you can mouse hover over that word (e.g., dissidents) to see what is giving rise to that situation and what preferred ideology their people prefer. For example, for your civ, it might have shown that one ideology had 4 "sticks" of influence over you (2 sticks each from 2 civs) and a second ideology also had 4 "sticks" of influence over you (2 sticks from 1 civ and 1 stick each from 2 other civs) and that your people's preferred ideology was the first one. Unfortunately, in this example, switching ideologies to the first one does nothing to improve your situation.
Since ideological pressure comes from relative tourism/culture imbalances, you have to go to the 4th tab of that screen to see where things are. For the civs that have 2 sticks of influence, that probably means your culture is unknown to them (level 1), while their culture is familiar (level 3) to you. For civs with 1 stick, there is just one level of difference. That screen also shows how much base tourism each civ is producing and what tourism modifiers (open borders, trade routes, etc.) are in effect for each pair of civs. If you play around with that screen, you will soon get the picture.
That picture may show that the easiest way out of your predicament is to get your culture to be exotic with 3 or 4 civs ASAP, and that you are within hailing distance of that. Get open borders with this civ, send a trade route to that civ and you may be out of the woods in 10+ turns. Of course you also want to slow down their progress vs. you, so pump culture as much as possible. Ally a cultural CS, etc.