You need to go see your primary care doctor
or your OB GYN doctor right away. There are several different things that could be going on, but in order to figure things out you need a physical examination by a medical professional.
The fact that your boyfriend has a cold sore is concerning, as cold sores are caused by the herpes virus, and this could definitely be passed to the genital area. You are right that usually this causes small blisters to form, but sometimes these might not be easily visible. Also, if you had a cut on the skin of your labia, the herpes virus could get in there, causing an atypical infection.
It is also possible that you have an infection in the skin surrounding the areas where you had the cut on the labia. If so, in addition to some discomfort, there would be redness and warm around the area of the cut.
Another possibility is that you might be having a reaction to the neosporin that you are using which, believe it or not, is quite common.
Make an appointment with your doctor right away. They will be able to help you fix this problem.