I have a bump at the base of penis that looks + feels like a zit. hurts to masturbate, doesn't hurt to pee. what could this be?

May be just an acne: It's most likely just an infected hyperactive sebaceous gland like an acne on the face. Its occurrence will not affect how you urinate, but give you some local pain & irritation. It tends to recur once infection once took place; so, it may require surgical ablation or excision. But, without inspection / palpation, it's still hard to give an accurate Dx. So, see Doc for sure detail and care. Best..