Some do (eg BA), some don't. A Class 1 should be enough for most airlines that you are fit to fly. BA look at each case individually and I'm pretty sure yours would be no major concern. I know that there are people who've got on the BA cadet scheme having had a depressive episode requiring medication.
Read my post on the other thread concerning this. That should give you some insight and a comparison of a much more severe problem.
You do not have to worry about this in my opinion, clearly the problem if any was very mild.