Welcome to the STD forum. I'll try to help. The bottom line is that you no longer have any worries about syphilis. You are cured.
You were over-treated, in that most experts rely on a single dose of long-acting penicillin, which is what CDC recommends. Your second dose a week later certainly didn't hurt (well, it might have hurt your buttock a little bit!) but most likely made no difference in long term outcome.
Within 24 hours of the first dose of penicillin (maybe as little as 6 hours), all syphilis bacteria in the body are dead. However, it takes time for inflamed tissues -- lymph nodes, skin rash if there is one, etc -- to become uninflamed. Finally, some enlarged lymph nodes, whether due to syphilis or any other infection, never return to their pre-infection size. Indeed, most people have lymph nodes that can be felt in the groin, due to past infections in the legs, feet, etc (mostly not due to syphilis, of course).
As for the spots on your hands, they could be manifestations of an early skin rash due to secondary syphilis. The rash of secondary syphilis can actually become more prominent after treatment than beforehand. However, that usually is brief, and normally the rash of syphilis would be completely gone within 1-2 weeks. So most likely the red spots are not at all related to your syphilis. If they persist and you are convinced they are new, show them to your doctor.
With or without syphilis, your negative HIV tests 10 and 13 weeks after your last possible exposure are definite evidence you weren't infected. And your negative chlamydia and gonorrhea tests also are completely reliable.
If you are in the US, perhaps your case was reported to the local health department. I hope so, and that you cooperated in helping identify your recent sex partners to be sure they get syphilis blood tests and treatment. If not, please call the health department yourself and discuss it, and also call your partner(s) to make sure they are aware of the risk of syphilis. (If you have already done so, congratulations for your responsibility and thank you!)
Finally, stay safe! Please select your sex partners with care and use condoms consistently.
I hope this helps. Good luck-- HHH, MD
Thanks for the reply this really puts my mind at ease. Yes I helped identify my partners and from now on will use condoms all the time, I've mainly seen girls from college and thought it was a safe place, but I was wrong. I guess you can never trust someone unless you are in a long term relationship.