Thank you for your query.
Injury results in inflammation.Depending on the severity of the inflammation, the structures involved and the type of injury, the time to heal varies widely.
In your situation, you have fallen down the stairs and its possible that you have had repeated bumps (on each stair) on the areas you mentioned (neck shoulder, elbow).
I recommend using anti inflammatory topical preparations along with anti inflammatory tablets.
If there is swelling or muscle spasm, additional muscle relaxants , ice and hot compresses help.
APply hot compresses to the affected areas before applying the topical preparation.
MAssage the medicine gently . do not knead or massage hard.
Apply Ice pack after an hour for about 20 minutes (few seconds on, few second off). Repeat this thrice a day.
Rest your shoulder and do not try to lift it straight up.
If you have to lift your arm, make sure it is along your body (the inner part of the arm should be in contact with the side of your chest. after a certain point when you have to lift it more than 90 degrees, use a wall for support and crawl your fingers up and down - this will take the weight of the arm off your shoulder). Ideally, avoid lifting your arm if it hurts.
The same goes for your neck. when you move or turn, do it in a controlled manner. No jerky or sudden movements. The same treatment for your neck. When you apply the medicine, do so in a circular manner and include areas a couple of centimeters beyond the affected area as well.
Avoid driving, standing if you take the bus or train (sit and use your other arm for support) . dont hold your phone between you neck and shoulder. monitor your posture ( do not hunch ). check your pillows (especially if the pain is worse in the mornings)
If the pain doesn't get better in a week or it increases , please consult a doctor in person right away.
Hope this helps and you feel better soon.
Kindly let me know if this was helpful and feel fee to get back to us if you have any further queries.
Wish you good health