Can HIV Be Contracted Through An Open Wound?

Question : Hi, my question involves possible HIV transmission/exposure. Now I do typically battle OCD tendencies, but after an incident that has recently occurred, I would just like some peace of mind. A couple of nights ago, my girlfriend and I went to a local drug store to get her a thermometer because she wasn't feeling so well. As we were checking out, I noticed some blood (not sure if it was dried or not) on the top part of the cashier's finger. Now, I hate to pass judgement but it's hard to look past the statistics on XXXXXXX men and hiv. I think it's like 20% of XXXXXXX men are hiv positive? At least that's what I've read. Anyway, this man...to my best judgement, was clearly XXXXXXX (looked like a sickly XXXXXXX bowie/long hair, painted nails, makeup). Plus, we live in a very XXXXXXX oriented neighborhood in XXXXXXX Anyway, what are the chances that either my girlfriend or I became infected due to the blood exposure? I happened to have no direct contact with the cashier, but being OCD, I'm still freaking out for myself based on indirect contacts. I'm especially worried because my hands are quite chapped/dry from the winter and I'm a hand washer. Much to my chagrin, my girlfriend thought I was crazy for the immediate worrying (although she still loves me). I tried to get her to dispose of the thermometer. However, she proceeded to use the thermometer(which was packaged) despite my plea not to based on the possible blood on the package. In addition, neither of us were able to wash our hands for at least a half an hour after the incident. Because of that I'm concerned other things became infected (car keys, wallets, car cup holder, credit cards). So, with all of this said, and say hypothetically this man was HIV positive, were my girlfriend and I at risk based on what you've heard? I'm specifically freaking out about my girlfriend's use of the thermometer. Your answer and thoughts would be so much appreciated. And I thank you for your time. I know us OCD-ers aren't the easiest to work with. There is just a lot of information/forums on the internet that discuss exposure risks and length of time the virus is active outside the body. Anyway, I figured I would ask an expert instead of endlessly researching the web. I also plan on seeking some group counseling for my OCD tendencies. I don't want them to dictate my life on cause me to pass judgement on certain groups.