Is this "burning to the touch sensation" after miraDry normal?

I suggest seeing your physician for a formal evaluation. It's difficult to answer this without an in-person evaluation. Botox can also be used to treat excessive sweating. Best, Dr. Emer

It takes 2-3 months for the nerves to heal and it sounds like you did have some inflammation or insult to the nerve and a module as a result of the procedure (all fall under expected potential side effects). Nodules that are painful need to be evaluated by a dermatologist. If there is suspicious of an infection then an antibiotic would be given however this is very uncommon- I have not seen a true infection from miraDry ever. Often these nodules are purely inflammatory and resolve on their own within 2-3 months. Best of luck. 

1. The burning to touch feeling can occur. However, usually it is numbness most people get that disappears. 
2. With regard to swelling that is very common. 
3. Infection post treatment is quite rare, I would recommend that you go back see your provider.