Hello,
From the symptoms it looks like an allergic reaction to Amoxicillin. Please stop taking it and consult your doctor for a change in prescription. You can take over the counter antihistaminic like Benadryl or Claritin for itching. Application of calamine lotion is also soothing. You can apply 1% hydrocortisone cream like dermacort on the itchy areas. If symptoms persist then please consult your doctor. Oral steroids are needed.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
It very well could be an allergy to the med you took for the sore throat...the Amoxicillin. Many drugs last a lot longer in our bodies after we have finished taking them, so that has been 2 monhths isn't all that alarming. Benadryl is often used for allergic reactions.