I have read your question,
are quite effective drugs and they do their job.
Without physical examination It is difficult to conclude anything .
The Drugs Levothyroxine and metformin Surprisingly don't appear to show side effects that frequently , yet sometimes they both show similar allergic side effects which include :
1) swelling around the face ,lips and neck.
2) Rashes on the body
3)trouble in breathing and itching as well.
But these are the effects that appear only on Over dosage.
As you have mentioning itching ,yes it is one of the adverse effects of both the drugs ,there is a possibility.
I recommend you to Consult a Physician Immediately For further guidance . I assure you that the side effects of these drugs are rare hence there is nothing to worry much.
wishing you a Good health,