You're girlfriend needn't worry.
HIV cannot be transmitted by mosquitoes. Here's a link that explains why
...published by the Entomology Dept. at Rutgers University: http://220.127.116.11/search?q=cache:r...hl=en&ie=UTF-8
The boards don't make links "clickable" anymore so you'll have to copy and paste the URL into your address bar.
Regarding bird droppings, again, your girlfriend can relax.
I think the confusion about HIV and bird droppings comes from the fact that there's a fungal infection called histoplasmosis that usually affects the lungs. This fungus lives in soil, especially soil that's enriched with bird droppings.
If someone who already has HIV
or whose immune system is compromised in any way develops histoplasmosis, it can lead to very serious lung infection.
Since I presume your girlfriend is healthy she needn't be concerned one iota.
Bird droppings per se are "dirty" just like any feces from any "critter" but as long as she washed her hands, like kehorner said, I doubt that having dry excema would make her susceptible to any infection (bacterial) from the droppings.