Too embarrassing to ask my family doctor: I woke up a few weeks ago because my penis was itching. I had two places where what looked like two "boils" had suddenly come up. It was red and I popped both of them. I have been applying an ointment called Muprocin, left over from another (unrelated) time. It has been slowly healing and is mostly gone now. The surface is smooth, but it feels like muscle soreness localized where the abrasions were. I did a little research on genital warts and I don't think that's what it is. Is this an STD or could it be a spider bite or something like that? Should I go see my doctor about it?

Muprocin is anti-bacterial, so is useful only for that. Which is not to say it was a bad idea, because popping boils isn't really a good idea unless you are prepared to keep the raw skin underneath scrupulously clean day and night.
Anyway, I would just GUESS that you don't have an STD, but there's always a chance. If you even think your sexual history could mean you have one, you might as well get tested anyway.
Spider bites do leave huge raised inflamed areas that often itch. Some spread out over a wide area; I had one that was a big white volcano with a big hole in it. And they do like hidden moist areas to bite.
(I didn't know mine was behind my knee until a rash spread all over my leg and I ended up in the hospital with cellulitis. Always wash any opening in the skin with soap and water, a simple prevention of bacteria entering the body.)