If I am using my call data plan, not wi-fi, via my iPhone, and I turn it off and then on again will I be using a different dynamic IP address? If not is there a way to change IP addresses?
There is no way to select the network address on the carrier network. Most carriers run CG-NAT in order to have huge net blocks to draw IPs from. These IPs often correspond to "real" assigned IPs on the net but the carrier is using them like private IPs and NAT-ing to the rest of the world so there are no address collisions.
All that to say, you get what you get from the carrier network.
Do you have a specific concern about your address?