I have an iPhone with US Cellular and I want to switch to Verizon, can I still use my iPhone?

Will I have to get a new phone? I really don't want to.

Yes, you will have to get the phone Unlocked though. That will cost you anywhere from $20(sketchy) to $100. It's a weird process and can mess up your phone when someone does it that doesn't know what they are doing.

If you sign up a contract with Verizon, you'll have to get a phone from them even if it's free. You can sell that phone and flash your iPhone to the Verizon network and you're good. If you need help with getting the phone flashed to Verizon, mail me for references.