iPhone 4 Replacement Issues

I was having some trouble with my iPhone 4 battery life, so I took it to Apple to have it looked at two days ago. Turns out, my battery was shot and needed a replacement. I backed up all of my data/synced it with iTunes for when I was given my replacement yesterday. When I got my replacement, I synced it with my iTunes and all of my data/apps/contacts were back. But last night I was having problems with my phone (different issues than before). When I open apps, they automatically close down or close down while I'm using them, my phone will freeze for up to 45 minutes with a black screen and the little loading symbol and it will shut off on it's own. I've tried restarting my phone, re-synced it and even today I'm having the same issues. I had another appointment with Apple today for this issue, but the tech told me it might just be the software. It's getting quite frustrating because I never had an issue before the replacement and I can't even use my phone because of the issues it is giving me.

Any suggestions on what I can do to resolve this issue? I don't want to get stuck going to Apple again and not getting any sort of answer or help.

Thanks!