Thanks for your question. Your photo looks like you could have a condition called angioedema. You should be evaluated by an experienced board certified dermatologist. This has nothing to do with your Botox. Best of luck to you.
An allergy to Botox is very rare and at 2 months since your injectables it is almost certainly unrelated. Botox lip injection is not a standard procedure to have done either.You should consult your local doctor to try and work out what is going on.Hope you get to the bottom of it.