Blisters usually do break on their own eventually. It's not necessary to remove the loose skin, but you can if its causing problems.
The reason you don't break them right away is that the skin underneath is especially vulnerable. Since you let them break on their own, they had a few days to start healing, so that helps.
Now it's very important to keep that area clean and dry. Hydrogen peroxide is a good antiseptic, and has a reassuring (if stinging) "fizzling" action. Rubbing alcohol can also be used. Gently clean the area and put an antibiotic ointment (like Neosporin) on the blistered area every time you change the bandage - which should be at least once a day. If the bandage gets very damp with pus (oozy stuff) change it again. Also, wash your hands well before you touch the blisters.
If you've gotten this far without an infection, you're doing well. Keep it clean & as sterile as possible, and you'll probably be fine.
That said, do not mess around if an infection does occur.