I also started dancing because of relationship issues -- a lot of people do.
But even though the relationship evolved (ended), I fell in love with the dance itself. That could happen to you, too.
How to start? Hmm. If ballroom is what you're into, you might want to try finding a nearby USABDA chapter. The chapter I belong to publishes a list of local dancing venues, as well as a list of reputable instructors. Reputable is important. There are a lot of sleazeballs out there.
Then the question becomes private versus group instuction. If you want to become a fabulous dancer, the best and quickest (not quick!) way is to get some private lessons. But, if you're not sure yet, that can be a hefty investment. My recommendation is to try to find an independent instructor that gives short-duration, small group classes. Where I live, there are quite a few that give six to twelve week 'intro to ballroom" type classes with six or eight students. That way, you get to meet some new people and try dancing without having to jump in at the deep end. It's also a good way to "interview" a potential private instructor and to start tapping into the ballroom network around your town.
Incidentally, many of these instructors are not "strictly ballroom," and also teach swing, salsa, C&W, Argentine tango, etc. And even if not, they'll usually refer you to someone that teaches what you want to learn.
How you continue, I think, will depend on your goals. Do you want to be a social dancer, just dancing to have fun and meet people, or do you want to be a great, technically excellent dancer one day? You probably don't know yet, so the important thing is to start. You can always decide later.
