You don't mention where you experience pain when you have sex. If it is vaginal pain, I would suggest you see your family doctor to get a physical examination, including a Pap smear to rule out anything physical. You can discuss this in more detail with your family doctor or ask for a referral to a gynecologist.  On the other hand, if your pain is related to your RA, check out this post regarding relationships and sex which contains links to a couple of places that have suggestions for positions that may reduce pain.

The reason your RA is not slowing down is because you're not taking your medication as prescribed. In order to prevent permanent damage to joints, you need to get your RA treated.  I cannot emphasize this enough: to get better, you need to take your meds.

Yes, immunosuppressants can cause sinus problems and the Biologics are especially hard on the sinuses, but they can be completely manageable. I wrote a post last year about managing side effects that you can find tips in there on how to deal with the sinus problems. I've been on Biologics for 4 1/2 years now and by using the techniques I described in that post, I've only needed to be on antibiotics for sinus infections a few times in that period. Whenever I feel my sinuses getting inflamed, I increase my intake of pineapple juice, garlic and water and rinse out my sinuses with salt water and this way, I have been able to beat back an infection numerous times.  As well, the latest research shows that most sinus infections resolve on their own without needing antibiotics, so that's a good thing.

in terms of Prozac and the other drug you mentioned - it is common to experience depression when you have a chronic illness such as RA and especially when your disease is not well controlled.  You may find that once you get your RA under control, your depression will lessen.