I phone SE shows 100% charged - shuts off - then shows only 10% charged

I have a I phone SE that I love. It has plenty of storage space - and I like the smaller size.

In other words, no need to upgrade.

However, the phone doesn't seem to be charging properly.

When I go to bed, I plug the phone in. When i wake up, it shows 100% charged. I begin to read the news, and bang - it goes out. When it restarts (which is seems to do on its own), it reads 10% (or some minimal amount) of charge - generally the same as the night before BEFORE i began charging.

do i need a new battery? Other?

Thanks in advance.