He might have a infection, which if so is VERY SERIOUS! Dark streaks or veins can mean blood poisoning and that needs immediate attention.
If it is more like just a bruise from getting hit in the leg or something thats not anything too much about. I would ice it if this were the case.
I sounds to me like there was a spider bite, or infected ingrown hair. Either was MRSA is a very common infection these days. I is very dangerous and can be even deadly so it is very important that he sees a doctor asap if you think it is looking in any way infected.
Good luck and I hope you talk him into going!
If your brother-in-law has varicose veins and is on his feet all day, he could have developed a blood clot. In the absence of a wound causing infection and fever, that's my best guess. A blood clot can be just as dangerous as an infection because pieces can break off and go anywhere in the body like the brain, heart or lungs and result in a fast death.
Your brother-in-law MUST see a doctor as soon as possible. I can't tell you how foolish it is for him to ignore this problem. I am not a doctor nor are there are any doctors on this forum, but I've seen the speedy and deadly results of blood clots, brown recluse bite infection and wound infection and can tell you this sounds like a legitimate emergency. What is his objection to seeing a doctor?