First, I don't think the new sores on the other side could be syphilis, because those don't sting nor hurt. And if after six weeks, which is the window period for that STI, the result is negative I wouldn't worry at all.
Second, on my first OB I got sores in the foreskin and a small one in the head.
In my 3rd OB, which got cured a few days ago, I got sores in the shaft, near the groin, so not even close to the original OB, So yes, I think it can be normal that you're getting sores in other places. Don't worry, it's a process and I think it hits each person very differently.
Regards!