We live out in the dairy preserve area of Chino, CA, so we have a TON of spiders here. Everything you've described sounds EXACTLY like a spider bite. By the way, Indomethacin is just another NSAID like Piroxicam. That's it. It will not help much for a spider bite except, in hopes, of getting swelling down. He needs an antibiotic right away (doctors should have known this, should have given him AB's, along with the anti-inflammatory) if not an IV of antibiotics. The way you've described what his foot looks like, describes the same way my husbands foot looked when he was bit by a spider! And we can't necessarily find the spot we were bit at, either. A lot of doctors will say, "Well, I can't find any spot that tells me you were bit by anything.". That is a crock. Especially if it's swollen the way you've described it, red, warm, etc., etc.......it makes it that much harder to find a bite mark.
I suggest you get a bit 'pushy' with these doctors, find a second opinion if necessary ( and NOT in the same medical group as these doctors will always agree with their colleagues), and make it clear to them that you do have violin spiders (aka: brown recluse) AND black widows, etc., etc.. I'm thinking it's one or the other. A brown recluse bite, though, is worse than a black widow, leaving you with fevers, excruciating pain and wishing you were dead.
Please, if his foot is still the same today, get him to a doctor ASAP. I know I have not seen the foot at all, but what you describe tells me there just might be an infection.
Good luck and please keep us all posted.
Terry