You can try taking a hot bath to relax a bit. Ice will bring down the inflammation, you can alternate ice and a heating pad.
You can take tylenol, but really thats just a bandaid, its not going to bring down the swelling.
They don't have to be visibly swollen to have inflammation. Its inflammation in the joints that causes them to hurt. Crohn's can cause your joints to swell/become inflamed so treating the underlying cause (could be Crohn's or could be arthritis) will help reduce the inflammation and stop the pain (or at least reduce it dramatically). Be sure to inform your GI that your joints are hurting a lot because its possible that your current dose of Aza isn't enough. There are also other medications out there that can help with joints pain if you have arthritis that also treat Crohn's (Humira, Remicade etc). Getting a referral to a Rheumatologist can also help even if the joint pain is caused by Crohn's (I recommend it).
For now as mentioned you can alternate between hot and cold (ice packs, heating pad, hot bath etc). If Tylenol doesn't do anything for the pain then you could ask your doctor for something stronger (I take Tylenol 3 for my arthritis pain as I have osteoarthritis).
I just seen my doctor/ specialist about the same thing, actually in the same exact places that uou mentioned. I was not experiencing any inflammation or swelling either. The doc said it wasnt arthritis, and it was probably due to the Crohn's, I am currently having a flare and the joints just started goin. The doc says it will go away when the flare gets under control. Are you currently in active disease? Or having a flare? This could be the problem.
I pretty much rely on hot baths and Tylenol. I don't want to take any opioids and MMJ isn't legal in my state so Tylenol is all I have. It gets me through the work day which is what is important to me while we try to get this flare under control.