My boyfriend had a cold sore and now I have what looks like a rash on my pubic region which I'm not sure if it's from his cold sore or a shaving rash?

Possible. Assuming that his oral lesion was herpes, it would be possible for him to transmit the virus to that area of your body through oral sex. However, Herpes looks more like ulcers or vesicles rather than a flat red rash. Your doctor can easily tell the difference and test for it.