The answer to your question is simple.....Yes! Anxiety is famous for causing dizziness, weakness and that woozy feeling amoung a very long list of other symptoms it causes, everything from as minor as dry mouth to feelings of having a major heart attack...
You have had a check up and all has come back fine so maybe your next port of call would be to get some therapy for the OCD and HIV phobia..... maybe therapy in the shape of Cognitive Behavioural Therapy, where you will learn to control your thoughts and actions and better understand why you act and think the way you do.
I hate when doctors give an EKG for these symptoms...An EKG will only detect if you are having or have just had a heart attack. Nonetheless, yes you have anxiety. I have the same symptoms as you do, and the more you worry the worse the symptoms will become. You can even pass out from anxiety. I myself have not passed out, but I have come close once. It is good that you went to get checked out at the doctor and now you have to try to not worry so much. I know that sounds goofy to someone who is an OCD, but you have to just know that there is nothing seriously wrong with you and you are going to be ok. This will reduce a lot of the symptoms you are having over time. It is also important to note that these symptoms you are having will vary on how long you keep them. I have been dealing with the exact same symptoms you are having (plus a few others) since July of 09. Good luck to you!
Anxiety can cause a multitude of symptoms in my opinion to include what you are describing. In my experience with this, we also tend to focus on symptoms that justify our diagnosis of what is wrong with us. You did the right thing by going to see a doctor about this; now you have to believe him/her. Do you have access to counseling. By learning about it, it becomes much less confusing and scary and can help you confront it and get through it in my opinion.