Mom, I know exactly what you are talking about - I've had that happen as well. I believe when I had a similar problem I was on mtx as well as sulphasalazine. I fear I might be a candidate for skin cancer because my arms and chest have burned constantly due to sun sensitivity. I'll stop to talk to someone in the parking lot for 15 minutes and have a sunburn (granted, I also live in SoCal). I also recall even covering up in clothes I felt like the sun was burning me - similar to your story. I think jeans are so thick and absorb the heat, it doesn't help.
I would STRONGLY recommend you wearing a big floppy hat or a bucket hat to help keep you shaded as much as possible if there is no shade to retreat to. Also, if you are in a suit, cover yourself up with the towel periodically to keep yourself shaded as often as possible when you are out of the water. Of course, use the strongest sunscreen you can find as well. Remember, technically, if it is SPF 50, that means you are supposed to reapply it every 50 minutes.