As you've been advised, seeing a doctor is your next course of action. We've answered your questions fully as far as our online volunteers can.
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1) Are these groin/testicular pains from Chlamydia or Gonorrhea due to the rimming I received?
There is no way to know that. Only testing and examination can tell you that. You could have anything from prostatitis to a hernia to maybe an STI.
2) Do I have Chlamydia, Gonorrhea, or even syphilis from this rimming exposure (even with cuts involved)?
Only testing can tell you for sure. Since you are so concerned, just go test. Make sure they do anal testing since you received rimming. The chances are low with rimming, but it's still possible.
3) Would I DEFINITELY have burning during urination or discharge if it was Chlamydia or Gonorrhea?
Not if you only have an anal infection and it hasn't spread to your urethra.
Really, you have symptoms of something, and need to see a doctor. Testing is the only way to know what you have. DO NOT try to treat this yourself. The treatment for gonorrhea and chlamydia is different, so get tested, see if you have something, and get the proper treatment if you do. Worrying does nothing.