I have painless bumps on the underside of my penis that won't go away. I have no other symptoms of an std.

Probably normal. There are many benign skin conditions observed on the penis that usually do not require any treatment. If it is bothering you, please see a dermatologist or an urologist to get a diagnosis and further advice. Hope this helps!
Go see your doc. You need to see your doctor. A bump on the penis could be a wart, syphillis, herpes, or an ingrown hair. Good luck.