Best way to heal strained/pulled neck muscles & resulting pain/stiffness/soreness? is ibuprofen a good choice? how long does healing usually take?

Ibuprofen, rest: Depending on any medical conditions (kidney problems, history of GI bleeding or ulcers) and assuming you are not on any blood thinners such as Coumadin, (warfarin) ibuprofen is the right med. I do not know your weight, but ibuprofen 600 mg three times a day with food for the next 10-14 days would be safe and beneficial. Also rest with light stretching. Typically takes 2-3 weeks to heal up.

Aleve (naproxen): works better for pain resulting from muscle inflammation. However, you should see your GP for proper diagnosis and management.