My doctor prescribed some medicine to heal my canker sores faster. Is this healthy or is it healthier for me to just let it heal on it's own?

Use the medication. The medication is fine to use. It will not harm you and it will help you feel more comfortable faster!
Just another option. Yes the medicine can help cut the cycle down in number of days. If you don't like medicines and can tolerate the discomfort you don't have to take it, but will take 14 days for healing on its own. Discuss laser as an option with you dentist for next time the canker sores startto appear.
I'm sure you will. Appreciate less scarring right? Apply it please.