Hello and welcome to e health forum.
In case, he was indeed infected, the risk of infection would be slightly higher, since there was bleeding gums in your mouth.
The symptoms described by you are not due to HIV.
The described rash is also not due to HIV
Whether a person has HIV, it can be determined only by serology tests for HIV. Occurance of dengue and jaundice in person , does not make him immunosuppressed or prone to HIV.
In case you are so anxious about HIV, then getting tested for HIV after 1 month post exposure, with the HIV Duo test, might be helpful to relieve your anxiety.