Dear Bee,
Welcome to the Wefugees Community and thank you for your question.
The "Aidshilfe" provides very useful information at their website. They state:
People with HIV can, in principle, work as doctors or nurses without any problems. Limitations only apply when there may be a risk of infection for other people. It's important to make sure that no blood from the doctor or nurse can comes into contact with a patient’s wound. This, however, is already covered by the normal hygiene procedures.
A risk only exists in a very small number of specific surgical procedures that carry an increased risk of injury for the surgeon; for example, when the surgeon's field of vision is limited and the scalpel has to be guided with the finger. In rare cases, similar situations may occur for dentists, gynecologists and nurses.
People with HIV are not allowed to carry out these procedures. This does not mean, however, that they are not allowed to work in the profession."
And the website "Positive Destinations" collects information on travel, visa and immigration topics for people with HIV. See here, for instance, the country profile of Germany which explains that Germany does not have any restrictions on entry or staying for people with HIV.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,
Meike