Dirty needle sticks are a scary thing, and I'm sorry you're going through this time.
HIV actually isn't very easy to get. Hopefully this helps ease your mind at least somewhat:
The Occupational Safety and Health Administration (OSHA) estimates that of the some 800,000 injuries each year, only about 2 percent (approximately 16,000) involve needles that are likely to be contaminated with HIV. Of those 2 percent of needlestick injuries where HIV-infected blood is known to be present, the chance of HIV transmission is estimated to be between 0.3 and 0.45 percent.
Even IF the patient was HIV positive, for sure, without a doubt, you would STILL only have an 0.3-0.45% chance of catching the virus! And you definitely can't catch HIV from someone that doesn't have it. There is a window period where it doesn't come up in testing, yes, but it's very unlikely the patient was in that window period - HIV isn't THAT prevalent in the general population.