You used a condom for everything. There is no chance of gonorrhea, chlamydia, HIV, any of the hepatitis viruses, mycoplasma, trich, NGU.
There is a very small chance of herpes, syphilis and HPV - small enough that I wouldn't even worry about it without symptoms.
Has your new partner been tested? You could just suggest that it's a good idea to test together, and be safe, since you aren't using condoms.
Is this level of anxiety new for you? If it's not, have you ever talked to anyone about it?