How long before STD Testing? - Please read

My bf and I had unprotected sex for the first time Aug 1st. Then again on the 8th. Both times we started with condoms but took them off. After the first time I noticed some itching and a lot of left over lube. The condoms we used were super lubed up. I had itching after the second time too. I don’t have the best experience with condoms. The third time we didn’t use any. The irritation had pretty much subsided. I got tested for every STD on the 16th and everything was negative. I even had a pap. This was a new doctor’s office for me. Someone in there was complaining about the amount of lube that was used during their pap. So after mine everything was fine at first about 3 days later it felt like I had developed a yeast infection. I was itching persistently and my discharge was thick, white, and clumpy when I rubbed it. I didn’t have any in my underwear, I was just checking my CM because I was itching. I went back to the doctor and had a Urine culture done. They said I didn’t need to be tested again because it had been 2 weeks since our first encounter and neither of us had a new partner since then. I took some diflucan and my symptoms have pretty much gone away.

Does anybody think that two weeks wasn’t enough time for Chlamydia/Gon Testing?