I agree with Tonda.... and an antihistamine might calm things down. Sounds like a major flare up or even an allergic reaction too. Have you tried supplementing your regime with anti-inflammatory supplements ? I see a Naturopathic Dr and a RA dr. The Naturopathic DR has been a Godsend. Here are some things to consider but they won't work immediately but can add them to your daily routine - all are anti-inflammatory supplementation:
Tart Cherry Juice (available in a bottle at Vitamin Shoppe or other health store) & comes in gel form. Omega 3 Oil - I buy PHARMAX brand via Amazon it has 1,975 mg. of the necessary Omega 3, I take a tumeric blend that is wonderful and it can be purchased online as welll ANTI- I.N.F. Natural Essentials I think makes it. When you are in a flare up, take 2 in the am and 2 in the pm. Also Boswella 500 mg. Eat Pineapple which is high in Bromelain (another anti-inflammatory food) or you can take the capsules.

Has your rheumy considered it being an allergic reaction?
I was on remicade for about 10 years and never experienced that. It did take several infusions before I began t feel any relief. It is possible that your are in a flare and that is what is causing the additional pain and swelling.
Are you taking any other medications with the remicade? Methotrexate? Steroids?
Does your rheumy give you any tylenol and antihistamine prior to the infusion?

Also of interest which might help calm you down - swollen joints do not necessarily mean joint damage. I have the luxury of working in the orthopaedic field and my hands/knuckles were swollen for a few weeks. I had an xray taken - DR said NO erosion, I was ok

Thanks for the ideas. Just had my 3rd infusion, They had to stop at the end because of an allergic reaction. Geez I am now very swollen like never before. Mh throat hurts, my body feels dead. My dr wants to continue? I don't think this is something I can do.