Well, anything is possible but I'd take a test if you are concerned.
Could it be possible that the spotting itself is my period since I did have a blood clot here and there and have had cramps and back pain
Spotting can definitely happen. If you take another test 2.5 weeks out from when you had sex last, you should count that test conclusive. Women are late all the time for a variety of reasons including stress, illness, weight gain or loss, changes in routine, etc. good luck
We aren’t ttc I’m just worried because I have never spotted before and it already lasted 6 days
Since you have had negative tests, it's really unlikely you got pregnant. Unless you tested too early which could be possible. You can get a positive test 2.5 weeks after the sexual episode. There are less likely times that a woman would conceive and having sex right as your period is due is a less likely time. Still a chance but slimmer. Are you TTC?
Anytime you have sex, it's possible you can get pregnant- when it's protected sex, your chances do go down significantly, but there still is a chance. If you had sex on May 13th, and you are worried that you may have conceived at that point- wait another week or two and take another test- that's the only way to know for sure. The spotting could be your period, it could be some form of implantation bleeding, or any number of other things- so just wait and take another test. I know it can be hard to wait- let us know if we can help you with anything while waiting or after you get the results!