Is it horrible to incorperate formula into feedings?

my newborn has been strictly fed since birth (is now 1 month), and I have som pretty horrible, sore and never healing . I only produce milk with one , so it doesnt really get a break at all...its in rough shape. It stings like someone is chopping my nipple off every time I feed, the whole time I am feeding and I cry from the pain. Would it be horrible for me to introduce formula mixed with milk into his diet? It doesnt hurt as much to pump, and milk is so much better for him, I dont want to strictly feed him formula. It makes me feel like a bad person to feel like doing this, I'm just in so much pain.