If a used syringe can transmit HIV, why can't a mosquito?
Answers:
There are two main reason why they don't transmit diseases like HIV.
1. Mosquitoes digest the virus that cause AIDS.
2. Mosquitoes can not ingest enough HIV particle to transmit the virus.
The source i provided goes into much greater detail, but thats the prevalent jist of it. Give it a read.
Hope this eases your mind...
Mosquitos are competent to carry enduring diseases (yellow fever, west nile) they are not competent to transfer the aids virus however because they are different virus and mosquitos don't have as much blood contact as a syringe would.