Hi, welcome to the forum, we can understand your anxiety related to the symptoms. If the barber has used a new blade then you need not worry about HIV. The symptoms of your clearly suggests bacterial infection.
The strong possibility of the growth is a carbuncle which is nothing but group of folliculities. It is commonly seen in back of neck. It occurs due to infection of the individual hair follicles. Coalescence of several inflamed follicles into a single inflammatory mass is carbuncle.
The choice of treatment would be incision and drainage procedure which will expel the formed pus and helps healing faster. Usually MRSA or staphylococcal bacteria are involved hence treatment with appropriate antibiotics is mandatory.
I suggest you to consult surgeon without delay for early treatment. Take acre and regards.
My guess would be ingrown hairs. I am not sure how to treat them, but that is what I would assume I had with the symptoms you describe. I think they usually grow out on their own though, but are painful in the process.