IF YOUR FEET AREN'T HAPPY, NEITHER ARE YOU.
Let's just snuff out a common misconception that boots are required for backpacking. Boots are great for providing ankle support and stability while carrying heavy loads, but thanks to improvements in technology we've seen drastic reductions in the weight of our gear. A pack that used to weigh 8 lbs., now weighs 4 lbs. Materials are lighter and stronger and without much effort, you can easily attain a 35 lb. pack weight for 1-4 days of backpacking that includes food, gear, and water.
Boots were required to carry heavy loads, but since that's no longer the case, a backpacker can get away with using a comfortable trail running shoe instead. Long distance hikers live in trail runners for good reason. They're more comfortable, require no break-in time, and they're more gentle on the feet. Even backcountry hunters have made the switch to trail runners for their activities.
If you're a boot lover, I know how it feels to give a shoe a shot in the mountains, but I encourage you to try it out once to see how it feels. If you don't like it, you can always go back. If you're new to backpacking and you're confused on what footwear is right for you, just grab your favorite running shoe and try that out for a trip.
Unless you know you're going to carry heavy loads that require extra ankle support, most trail runners will do the job just fine. Having wore trail runners for a few years now, it is very hard for me to switch back to boots when the situation calls for it. The freedom a trail shoe gives you is second to none.
Lastly, if you are battling blisters or foot pain, try a different shoe. Go up a size to give your foot room, air your feet out and swap socks often, and do your best to keep everything as dry as you can inside and out. If you feel a blister coming on (feels like a hot spot), address it right away before it gets too bad by covering it with tape or a common blister prevention method (you can find these in any outdoor store).
Taking care of your feet in the backcountry is huge. Your feet carry you and do all the work so take care of them in return. Blisters and raw feet can get infected quickly and can be very dangerous and incredibly painful to walk on.