If a mosquito bites someone with a very active HIV infection and bites me immediatly after can I catch HIV that way?

Absolutely no! Mosquito bites cannot transmit HIV infection. This is a myth!
No. This issue has been a concern since the onset of HIV ds. Studies conducted by the cdc and elsewhere have shown no evidence of HIV transmission through mosquitoes/any other insects. Mosquito does not inject its own/a previously bitten person's blood into the next person; it injects saliva. Hiv lives only a short time inside insect & does not reproduce or survive in insects.