Could changing acne products actually lead to rashes or more acne?

Sometimes. When you switch products for your acne, often you will experience a worsening of your acne until your skin has a chance to acclimatized to the new product. This can be frustrating. Also, most acne products are drying so switching products might mean you are now using something "more drying" than before. This would give you a reaction/rash. The key is to go slow when switching regimens.