You used a condom, therefore you had no risk. Oral sex is not a risk either. Even if she was HIV+ (which is highly unlikely and weird that you would assume she was) then it still would not be a risk. In an adult, the only risks for HIV infection are unprotected anal or vaginal sex and sharing drug needles with infected users. And since you didn't have a risk, obviously there's no reason to test.
You think your girlfriend (whether a month or not) could have HIV? She's hiding it? Come on. Talk to your doctor about anxiety. You had no activity that is a risk for HIV in the first place. The only way adults get HIV is from unprotected vaginal or anal intercourse or sharing IV drug needles. Saliva and air inactivate the virus.
As has already been said rather bluntly, that is not a risk. AIR inactivates the virus. Little cuts on the penis and tested are not ways HIV is spread. You do not have to take the advice to talk to a doctor about anxiety but if you do not, you probably will never have a normal sex life as you will just worry and worry over nothing until you drive your partner crazy. Do yourself a favor and talk to your doctor about anxiety.