You have previous posts talking about oral sex and vaginal sex, so I'm a little confused about the "no oral sex and no penetration" part of it all.
Heavy petting is no risk for STIs. There is no risk with fingering, mutual masturbation, etc.
If you had protected oral sex, there is a very slight risk for syphilis and genital herpes type 1, if you don't already have oral herpes type 1. The risks are low enough that I wouldn't worry about it. Most experts feel that one act of even unprotected oral doesn't warrant testing.
Protected vaginal has a low risk of syphilis, genital herpes type 2, and HPV. There's no test for men and HPV.
Again, the risks are low enough that without symptoms, I wouldn't test.
Check the guidelines for the HPV vaccine where you live. It's different everywhere, but you may be able to get it. It won't prevent or cure a present infection, but can help prevent future infections.