Welcome to the forum.
There is no risk of STD transmission from this sort of exposure; neither hand-genital contact nor kissing carries any measurable chance of infection. Your uregent care doctor was being unnecessarily conservative; no testing or treatment was necessary. Had your chlamydia test been positive, it would have had to be from some earlier exposure, for 2 reasons: you couldn't have caught it; and it takes at least 2-3 days before a chlamydia test is positive.
I don't know what it meant by "my penis does feel irritated". It's clearly not an STD, and I wonder whether you're just paying too much attention to your penis out of anxiety.
Here is a thread that explains the biological reasons why events like this carry no risk. Start reading with the follow-up comment dated December 14:
http://www.medhelp.org/posts/show/1119533
Regards-- HHH, MD