You are correct about the timing of your symptoms. No infection -- no STD, not HIV, and not even a garden variety cold virus -- can cause symptoms less than 24 hours after exposure. Whatever is causing your stiff neck and possible enlarged lymph nodes could not possibly have been caught during the rimming event the previous night. (Although I suppose a stiff neck could result if your head were in an unusual or stressed position during sex.) Further, most people who believe their lymph nodes are enlarged are found to have no lymph node enlargement or inflammation when examined by a health professional; self-diagnosis by medically untrained persons is very unreliable.
The risk of STDs from rimming has never been studied, but logically is low risk for both the oral and anal partner. Certainly I have never seen a case of HIV or other STD that was thought to be acquired that way. The main risk to the oral partner in rimming is intestinal infections, i.e. various diarrheal diseases or, in rare circumstances, hepatitis A. Finally, no STD causes the symptoms you describe.
In any case, your symptoms are not due to any infection of any kind that you caught by rimming. If they are due to infection, it is something you caught at least 2-3 days earlier. Of course see a health care provider if the symtpoms continue or worsen, or if you otherwise remain worried.
Regards-- HHH, MD
I should have said that all my comments about symptoms and risk apply to unprotected oral sex as well as to rimming, i.e. if you performed fellatio on your partner. But of course every sexually active person outside mutually monogamous relationships should get routine STD testing from time to time. Although your symtoms could not be from the events the night before, it still might be time for you to visit an STD clinic for routine evaluation.
Thank you so much for the detailed response. It is much appreciated.