What is my realistic risk of getting chlamydia or gonorrhea from putting an unknown status penis in my mouth for roughly 2 mins- was shallow mostly licking, did not really taste any pre-ejaculate, no contact with the back of my throat? I’m female by the way 

This is a low risk exposure.  I'll explain why:

1.  Most people do not have gonorrhea or chlamydia.  Far less than 5% unless there is something about this partner that you did not mention.

2.  Even when the do, most exposures of any sort do not lead to infection although oral sex is particularly low risk.  There are no scientific data on exactly how often a single exposure to an infected partner leads to throat infection but i am very confident that it is less than 10% of exposures to infected partners and probably substantially lower.

3.   Licking without introduction of the penis deep into the throat is a virtually no risk event.  As a generalization, no penetration, no risk.  Your risk sounds to be somewhere in between'

You asked about azithromycin.  There are good scientific data that 2.0 grams of azithromycin (4 times what you took) will cure mose gonorrhea.  There are no data on the effect of 500 mg although it is safe to say some but not all oral infections would be successfully treated by this dose.  Multiple doses would increase the cure rate

I hope this information is helpful.  I am not a better but, if I were, I would be comfortable betting a lot of money that you are not infected by the exposure that you describe.  If you wish to prove it, a throat swab for gonorrhea and chlamydia  at  any time more than 5 days after your exposure will produce reliable results. 

I would not be at all worried. EWH