Should I quit breastfeeding

My month old baby nurses every 3/4 hours because he sleeps for that long and it causes my breasts to get engorged, I try waking him up to feed but he rather sleep and I also have a two year old demanding my attention as much as he possibly can. My breast now on the left side twice has gotten rock hard and the first time a hot compress and massaging it helped but this time it's not helping at all and I want to cry when ANYTHING barely grazes it and that's ALOT with two Littles.

I just don't know if it would be easier to make a bottle when baby wakes up, instead of breastfeeding.. because even going places having my two year old I can't just get to the grocery store and feed my baby real quick in the car before my two year old throws a fit.

Help? Ideas:( id pump but still just too much to try and whip it all together while dealing with my two year old :(