Although no one can diagnose your problem over the internet, this is not uncommon in a number of viral infections, for one example, Herpes Simplex virus (HSV.)
Usually people are exposed to HSV - the virus that causes cold sores - as children; in that case, little ulcers in the mouth and on the skin around the mouth are common.
In adults exposed to HSV for the first time, the throat is more commonly affected, but lesions can be anywhere. It is interesting that you mention chicken pox-like lesions on your face, because chicken pox is also caused by a virus in the same family, Herpes Varicella virus. Your doctor might do cultures for HSV - which will ultimately go away - and at least you will have an answer. At this point, anti-virals would be ineffective.
Another virus - also in the Herpesvirus family - which causes prolonged throat ulcers/lesions is the virus that caused Infectious Mononucleosis (in this case the virus is called Epstein-Barr virus. Facial lesions are not part of this illness however. Again, a blood test can be done to determine if this is the cause.
Finally, this is also consistent with "Herpangina" which is caused by a number of viruses including but not limited to the herpesvirus family.
No one can tell you what to do without knowing the root cause of the problem and your personal medical history. But your doctor should be able to give you a pain medication compatible with your personal medical condition.
Edited to add: I realized that in my diagnostic frame of mind, I didn't really answer your question. I guess I was trying to reassure you that this, too, shall pass soon enough, and no further treatment would necessarily help. However, to answer your question:
Always check with your doctor before following any advice derived from the internet.
The following assumes no allergies, that you are a youngish adult in excellent health generally.
Maalox and Benadryl does help temporarily. Alternatives are lidocaine to gargle and spit, or Cepacol (can be sprayed or can be slowly released in lozenge form). Do not use in combination or in excess. These medications are meant to give you enough relief to eat and stay hydrated.
Gargling with cool water or warm salt water (1 tsp salt in 2 cups warm water) may help, as might eating cold foods. But these things will be temporary, and as long as there is deeper tissue inflammation, it will still hurt to swallow.
You will probably get more significant relief with a systemic medication, like acetaminophen or ibuprofen, For some, acetaminophen works better, for others, ibuprophen. Recently some doctors have recommend that you can take acetaminophen and ibuprofen at the same time because this has been shown to be as more effective at pain relief than either one alone. However, any drug should be taken only when the benefit outweighs the risk, and that applies much more so with combination drugs. All the usual precautions apply as well.
Note that some drugs are best avoided in some illnesses. Ask your doctor. That's why she's there.
Acute herpetic pharyngotonsillitis
Infectious Mononucleosis Clinical Presentation
Combining Paracetamol (Acetaminophen) with Nonsteroidal Antiinflammatory Drugs: A Qualitative Systematic Review of Analgesic Efficacy for Acute Postoperative Pain