Hey @Essa_,
Welcome to the forums! Sounds like you've got a lot on your mind. I hope we can help.
I'm 30 and I have bipolar II, which is on the same spectrum of disorders as cyclothymia. I've never had an eating disorder per se, but I have problems with impulse control in both my hypomanic and depressive stages, which often turns into overeating or imbalanced eating.
I'm on a combination of mood stabilisers and antidepressants. I've gone up about two sizes in the first nine months, which is probably partly from the meds, partly from overeating, and partly from being a couch potato while I've been off work. I've been eating better recently and I started a proper exercise program last month (gym and/or swim 3-4 days a week, going for a short walk on the other days). I feel much better and the scales are starting to swing back the other way. So all up, the meds alone have caused a bit of weight gain, but not much.
The meds also haven't increased my appetite. If anything, because my mood is more stable, my eating is more stable. I have more self-control and I'm better able to eat treats in moderation. My psychologist has also helped me learn to value looking after myself, so I'm more ok with cooking healthy meals for myself and holding off on some of the junk food.
So I guess my advice would be to try the meds and try whatever talk therapy your doctor suggests. The weight gain from the meds is not huge, and there's a good chance that treating your cyclothymia will also help with your concerns about food. And remember, there are lots of different of medications out there, and only some of them cause weight gain. If you start on something that's not working for you, you can always talk to your doctor about other options.
Good luck,
Fish