You can put any tire you like as long as they are not to big as to rub on the wheel well. Usually not a problem. Keep in mind that the speedometer and the power will be off slightly.
Your car should have a specific overall tyre diameter (or rolling radius) - the fact that the sump is getting caught means either the overall tyre size is low or the suspension is lowered (or very low to start with). It would help if we knew the make, model & year of your car & the current tyre size.