It is not necessarily going to be an easy road and you may have to jump through quite a few hoops. There is every chance that you will be able to obtain and keep a Class I medical (perhaps a special issuance). And it will probably cost a few thousand dollars to obtain by virtue of testing required.
Here is the FAA link that might help you. I strongly suggest you join AOPA and consult their medical team although there are other out there as well (e.g leftseat.com)
https://www.faa.gov/about/office_org...tidepressants/
Once you have a Class I, there should be no issue with any airline (even with a special issuance). The challenge is maintaining that Class I throughout your career.