It could be your hardware, but I suspect it's software related, which a new phone wouldn't correct.... and the nice folks at an Apple Store could do nothing but give you a replacement and hope that fixes it.
Does restoring as new do anything? (Erase and contents and settings and restore as new?)
When I got 10, I set up as new, and the phone was ridiculous battery drain with indexing, but then it finally leveled out after 1-2 days.... I'm only saying this because a new phone might go through that if you do get replacement or set up as new.
I dare not set up as new as I don’t want to lose texts, photos or video off my phone. I haven’t looked into iCloud backup yet as it confused the hell out of me last time. It’s definitely the update that did this, I know it’s not hardware. I’m not interested in a new phone, just want an update released that gives the phone back it’s performance.