See your doctor, and do the FMLA paperwork asap (I assume you have reached the one year mark since you're late grace). I have a buddy who works for a certain ATL based regional and he does FMLA all the time.
You don't want to keep calling in sick for multiple trips.
Once you do FMLA, then you are covered for however long it takes and it only counts as one "event"...so no matter how many trips you miss it's only one event. Also if your company has occurrences, I think FMLA cannot count as even one occurence.
Also call your union.
If you go outside your grace month for a PC, you simply cannot fly 121 until you complete the PC. I think that if you go over a year without flying or doing sim, then you might have to repeat all or part of your aircraft training.
Don't split hairs about where you live vs. your domicile...if you're sick, don't come to work, period. You don't have to debate with management whether you're too sick to fly, but well enough to do sim. You're sick...do FMLA and stay home.