Even though you gained height. You probably did not gain distance between the wheel, unless you moved the axles further apart. I will be surprised if you have enough space to go to 16 inch wheels. Even 15 inch wheels will need to be measured first to be sure they will fit without rubbing together. 15 in wheels with a low aspect ratio should fit but if you go with a high ratio they may not.
Measure hub center to hub center on the axle and then find out the diameter of the tires you are looking at to figure out if the tires will have a minimum of 1 in between the tires. 2 inches is better since as they heat up they will expand and 3-4 inches is optimal.