It is not possible to contact any STD by hand-genital contact. (Well, a few months ago a guy reported gonorrhea from hand-genital contact, but he said his partner seemed to intentionally massage her vaginal fluids into his urethra. Let's just say that's the only case of apparent hand-genital STD transmission I ever heard of.)
It sounds like you have hypospadias (if the abnormal opening is your main urine passage, i.e. the urethra opening on the underside of the penis) or perhaps a urethrocele. These are minor congenital abnormalties, and either one is susceptible to infection--and if either one connects to the urethra, it can lead to UTI.
UTI can be serious in men, so you need to see a health care provider right away--and then also follow your provider's advice about whether minor surgery is indicated to remove the abnormal passage, e.g. you might need to see a urologist. But STD is not likely to be an issue.
Good luck-- HHH, MD