If my iPhone 4 does not have a SIMM card can I only get service from the carrier of the phone?

The phone is Verizon, so I must go through Verizon?

Your phone is CDMA and it won't take a SIM card. So you've to go with Verizon or any CDMA carriers like Sprint, US Cellular, C-spire, Alltel, PagePlus, Virgin, Cricket, etc. If you need help with getting the phone flashed to any CDMA carrier, mail me for references.