Welcome to the Forum. I am not sure what the irritation that you experienced within a day of sex was but I am confident it was not an STI, nor a yeast infection. It takes more than two days and typically 3-7 days for symptoms of STIs to develop following acquisition. Further if I follow your post correctly, the irritation you experienced has persisted since that time. Is there visible evidence of irritation or infection at this time? If so, it might help to have a dermatologist take a look. In addition, I would suggest that you stop applying Neosporin, tea tree oil and other substances to the area of irritation- each of these can be irritating on their own and can make diagnosis more difficult. Besides what you have and are trying does not sound as though it is working. .
I also suspect that the white coating you have noted on your tongue is not related to the exposure you describe as well. Similarly, swollen lymph nodes, particularly in the throat or inguinal regions as you describe are non-specific finding with many possible causes. In fact, many people have lymph nodes that can be felt in the absence of infection or inflammation.
In answer to your specific questions:
1. Could this bump be herpes?
No, this is not HSV acquired through the exposure you describe. HSV symptoms do not occur so quickly and are self-limited. Even the symptoms of first episode HSV infections resolve within about three weeks of the onset of lesions.
2. Since this whole thing started less then a day later is its still possible that herpes took 50 days to form a blister?
No, it would be unusual for an initial episode of HSV to occur 50 days after exposure.
3. Does being on antibiotics make you more susceptible to yeast infections during sex.
Yes, antibiotics do increase risk for yeast infections. So do the steroid inhalers that you take for your asthma. Even so, most people taking antibiotics or on steroids do not get yeast infections.
My advice is that this has lingered on long enough and it is time for you to see a doctor who can examine both your throat and your penis to help sort out what is going on. I doubt that it is HSV and may not be a yeast infection either.
I hope these comments are helpful to you. EWH