Is not icing or taking medicine for sports injuries a bad idea?

No harm done: First, make sure you have a simple injury like a sprain or strain. More serious injuries like fractures need to be evaluated by a doctor. For simple injuries, ice of pain medication is to improve comfort. It does not speed healing. So choosing not to use these treatments is harmless, but it may increase your discomfort while healing takes place.

Typically: If you have any sports injury that is more than trivial, applying ice for 20 minutes every 2-3 hours for the first 48 hours helps reduce the inflammation which occurs. After 48 hours it is recommended to alternate, ice to reduce inflammation and heat to increase blood flow through the injured tissue.

Ice helps.: Icing and taking anti-inflammatory medications can only help virtually all sports related injuries. They both reduce pain and inflammation.