Can you get hiv through swallowing semen even if you don't have any cut or burns in the mouth or gums?

Yes, of course: Hiv is a sexually transmitted disease. Like any of the sexually transmitted diseases/std there are minor nuances of how they are contracted. However, the exchange of bodily fluids is common to all sexually transmitted diseases. Yes, semen is a bodily fluid. Please protect yourself, get yourself std tested and your partner. There are lots of websites on save sex, std/hiv.

Absolutely: Oral to genital contact of any kind can transmit hiv.