Should I be concerned with battery life at this point

Probably not. Depends if you're on 8.0, using the cell network, visiting sites with videos or java and so on. You used the internet a bit and that will burn your internet. Do some research on how to save battery life and you should be good. If your battery life reaches close to zero by the end of the day, you're doing fine as a guy with a new phone.

Yes, get that checked out. It's worse than mine and I'm getting mine replaced.