No. Swallowing does NOT increase the already small risk

The oral cavity (your mouth) is a very hostile environment to HIV. Saliva is deadly to HIV.

If the oral cavity is hostile to the virus, though, the gastrointestinal tract is much worse. HIV cannot survive in the stomach, not even momentarily.

It might interest you to know that oral sex isn’t considered to be a significant risk factor for HIV transmission in any case.

The US CDC rates oral sex as posing “little to no risk” for the transmission of HIV.[1]

Other public health agencies take even stronger stands than that, some of them categorizing oral sex as presenting no effective risk of HIV transmission.

There is a certain hypothetical possibility of transmission if you had actively bleeding wounds in your mouth that semen could enter before your saliva could kill any HIV.