Hi there. What you are going through is very common among people with OCD. Fear of germs and washing hands repeatedly is one of the most common problems that people with OCD experience.
A few thoughts for you:
HIV does not live for very long outside of the human body. Some say for a few minutes at most. Doctors who accidentally stick themselves with needles that have the blood of an HIV positive patient on them only get infected at a rate of 0.3 %. In other words, people who get a needlestick with fresh HIV tainted blood are fine 99.7% of the time. It's actually kind of hard to get infected by HIV.
There are other germs out there, but to get an infection, you normally have to get them into a fresh open deep bleeding wound or ingest a large amount of them. And even then, your immune system does a great job of killing any invaders. You need to develop a greater faith in your body's ability to fight off infection.
And the world (and you) is covered in bacteria and other germs. Some are actually beneficial (your digestive system would not work without them). By weight, your body actually contains more bacteria than human cells. Some are bad but they are held in check by the good bacteria and your immune system.
Washing your hands frequently is a good idea, especially before eating. Once every couple of hours (or right after touching something obviously dirty) will help you from getting sick. Washing ever 10-15 minutes is overdoing it. If you wash your hands too much, you can actually dry out the skin and have it crack open, leaving you more susceptible to infections with obviously counter-productive.
To answer your questions:
1. Yes, I would recommend seeing a psychiatrist or psychologist. They can listen to your story and give you an accurate diagnosis. If you see a psychiatrist (a medical doctor), they can prescribe medication that will help ease your OCD.
2. If you want to try going it on your own, I would recommend reading one of a number of books available about OCD. They will give you advice on the number of approaches you can take to fight OCD. Two that I like are "Worry" by Dr. Edward Hallowell or "You Are Not Your Brain" by Dr. Jeffery Schwartz.
3. Some psychiatrists do rely on a meds only approach. Some try meds with other treatments such as cognitive behavioral therapy. Psychologists are not medical doctors and cannot prescribe medications. They will try the other approaches. You will need to shop around and find a doctor who you feel a connection with.
On a final note, you may want to look into a product called Zylast. It comes as both a soap and a lotion. Both kill just about all bad germs (it was specifically developed to kill the Ebola virus) and has a residual effect of up to 6 hours. After you wash your hands with it, it continues to kill any germs that get onto your hands afterwards. The lotion does the same thing and does a great job of keeping your skin looking nice. It helped me get over the feeling that I needed to wash my hands as they were already covered with an "invisible glove" so to speak.
Hang in there. A certain amount of worry is good to keep us from doing stupid things. Too much worry is not good for you physically and will keep you from enjoying life. You need to find a balance and with some work on your part, you will.