If you are having protected sex, the chances of you getting an STD that would give you the symptoms you describe are very, very, very slim, unless a condom has come off or broken.
Frequent urination can be caused by a lot of things - a urinary tract infection, irritation to the bladder from foods, alcohol, caffeine, etc.
Stop squeezing your penis. If you get a discharge from an STD, you won't need to squeeze to see it - it will be there without you squeezing it. The penis discomfort could be from that. Your penis is your friend - treat it kindly.
Stop squeezing it for a few days and see how the discomfort is. If it lingers, see your doctor.
If you received oral sex from the woman, you could have NGU, which is an infection in your urethra, which can be caused by normal mouth bacteria. If your symptoms linger, you should bring this up to your doctor.