Kook, sounds familiar. Although I am generally a part time forum lurker, and not medically trained, I think I can help you on this one. A number of my friends and I have had this problem, and it has been discussed on other forums (like the FDL) over the years, although there is little info about it elsewhere and I believe that wetsuit makers are a bit negligent for not helping us with publicising info on this issue.
The problem seems to be a systemic (bacterial?) infection of some kind that has found its way into your glands in your armpits (I am not a physiologist but know the symptoms well). The fact that we (alone) use open cell rubber wetsuits, maybe combined with soapy lubrication of some kind that may open the pores in your skin, seems to make this a common issue for freedivers, although similar infections occur amongst windsurfers, etc. I don't think the problem is from a single exposure to bacteria, I now believe that it is exposure to bacteria that has grown in your wetsuit from the last time it was used, that causes the problem.
The solution that works for me is: Remove wetsuit ASAP after using, have a shower yourself or rinse off in fresh or salt water ASAP after diving, wash the suit (in detergent or antibacterial wash) and leave in direct sunlight to dry (do not leave too long or the neoprene will perish), store suit in dry place. Get a zipper or 'ducks bill' installed in your suit rather than peeing in it.
What I had been doing is a combination of: peeing in my suit, travelling home in the boat with it on (1 hour of perfect bacterial growth in warm and damp conditions), not showering for 6 hours, not washing the suit properly and not using anything to kill bugs, then leaving the suit a bit damp for the next time. Now that I have stopped doing most of the above, I have little problem, and if I do I stick more closely to my recommended behaviour and the problem is sorted out quite quickly.
Symptoms often start with small stapholoccocus (sp?) sores anywhere and will then progress to swollen glands, and boils under armpits in the groin, or behind the knees. A raised temperature is a bad sign. I got quite sick one time from this and a test of puss from a boil showed I had an MRSA infection (a very bad thing) but I got over it quickly with special antibiotics. Yuck. Now I am more careful.
Hope that helps and doesn't gross people out too much.