Thank you for your question, and I'm sorry to hear about your discomfort. It sounds very painful.
First, I think you could indeed be having a reaction to the hand sterilization liquid. Many people are sensitive to any number of things, and detergents and antiseptics (like in this liquid) are a common trigger of this sort of thing. Technically, it would be called a contact dermatitis - irritation of the skin, just based on that contact.
I don't think exercising has anything to do with it, at least as far as the ab/adductor machines contributing. But, this irritation and swelling that you have could certainly be aggravated by the warmth/moisture that can build up down there with exercise, and of course friction could aggravate it as well. Keeping the area cool and dry will help, and as non-aggravated as possible.
Sometimes people can develop jock itch, as well, which is a yeast infection (tinea cruris) in the area. If your symptoms don't get better in the next day or two, you should consider trying one of the over-the-counter preparations that are available for jock itch (lamisil, tinactin).
You can wait until monday. If it is contact dermatitis, keep the area clean, dry and cool (a cool compress like you're doing with the washcloth can definitely help), and see if it improves. Don't use any harsh soaps on the area. If, by monday, it hasn't improved, this may be a case of jock itch (here's an image of jock itch, if it helps -
http://www.hope.edu/academic/kinesiology/athtrain/program/studentprojects/405-03/dermatology/tineacruris_1_020527.jpg). Then, an over the counter remedy can help this.
If, however, you still haven't improved, or if you still aren't convinced, then give your physician a call. They'll be able to take a look, and start the appropriate workup. But I think waiting until Monday is just fine.
I hope this helps. Please let me know if you have any further questions - I'm more than happy to help.
Take care, and feel better - Dr. Fay
If I have helped, then please click the ACCEPT button and leave positive feedback - Thank you, and take care