Welcome to the forum. I'll try to help. But I have to assume you did not read the prominently labeled Disclaimer message or heed the advice there to look at other threads for similar questions. The exact ones have been addressed innumerable times.
The odds are low that your escort partner has HIV. When a woman is infected, the average risk of transmission to her male partners has been calculated at once for every 2,000 episodes of unprotected vaginal sex. Breaks in the skin generally cease to be significant portals of HIV transmission within a matter of minutes or hours, as clotting occurs and seals the wound, preventing access of HIV to susceptible cells. Having genital area cuts has never been documented as an HIV transmission risk. Finally, no infection of any kind causes symptoms within 24 hours of exposure, and for HIV it takes 7-10 days minimum; and HIV doesn't cause nasal congestion, sneezing, or cough. You caught a cold, perhaps from the escort -- but no more than that. To the specific questions:
1) See above.
2) I disagree there is a need for HIV/STD testing in this circumstance. You may choose to do so for the psychological relief of having negative results, but from a medical or risk assessment perspective testing isn't warranted.
3) Self assessment of possibly enlarged lymph nodes by medically untrained persons is very unreliable. Among many causes of enlarged lymph nodes (or other lumps under the skin), HIV is among the least common.
Get tested if and when you feel like it. But you definitely don't need testing later than 6-8 weeks; it never takes longer than that, despite common advice about 3 months or longer.
All these issues have been discussed in great detail innumerable times on this forum. Please spend substantial time searching and reading before asking any follow-up questions here. Thanks.
Regards-- HHH, MD