How do estus charges work?

The +7 next to your Estus Flask doesn't have anything to do with how many times you can use the flask, it indicates how strong it is (aka how much HP or FP it restores per use). The 10 is your number of uses (aka you can use the flask 10 times before returning to a bonfire). There are a few ways to regain Estus Flasks without returning to a bonfire, but they're not reliable.

Your number of uses can be increased by giving the blacksmith Estus Shards, and the strength of the flask can be increased by burning an Undead Bone Shard at the Firelink Shrine Bonfire.