How could I relieve the pain of a shoulder muscle strain without ibuprofen?

Hot or cold compress. Shoulder muscle strain can be treated with heat (or cold) as well as a topical rub. If just Ibuprofen is to be avoided, Naproxen may be a good alternative.
Tylenol (acetaminophen) Use tylenol (acetaminophen) and alternate applications of ice and warm compresses. Consult an orthopedist if things don't improve.

Related Questions

I have pain over the bony point of the clavicle at the left base of my neck with radiating pain into the pecs and shoulder. Muscle strain?

Complex Joint. The shoulder is a complex joint, & many conditions/ injuries (rotator cuff injury, bursitits, tendonitis, labral pathology, etc).Can cause pain/ weakness. Some injuries of the soulder occur due to acute injury and some are from overuse. Ii suggest you see an orthopedist for a complete exam. Read more...
May be more... The problem is a musculoskeletal issue but not a strain. If you have had any trauma to your clavicle, you may have a subluxed (mildly displaced) clavicle which leads to radiating pain in those specific areas. An xray might help demonstrate pathology. If you have no contra-indications, i would recommend scheduled nsaid's also to help with any inflammation that may be limiting recovery. Read more...