Clostridium, the bacteria that causes Tetanus poisoning, has an average incubation period of 3— 21 days with the average being 8 days. Lockjaw is a ghastly disease and nothing to meddle with, but I am fairly certain you have escaped it. It is still a good idea to have a booster though.
Thumbs are vital (yeah- I know that you have figured that out by now- being as you have been having pain for a month) and really you need to have it looked at to determine the source of the swelling.
I am going to assume that it is otherwise at least basically functional or you would have sought medical attention sooner. It is possible that you badly sprained it or it is infected but it is more likely that you fractured it and it just needs a splint and some R&R.
Hopefully it just needs more time. A bad sprain can take 6 weeks to heal. But the swelling is bothersome. Please consider seeing a medical professional.