A couple of days ago I went to a blind massage shop to doget a massage because there was something wrong with my left shoulder.

My left shoulder has been in pained and restricted in movement for several months.

I think that we only use the verb form "pained" with a person or a group of people as the object, and the meaning is not physical pain, but emotional. For example, "It pained Frank to see his son in such distress".

I initially thought it would be cured by itself, but ithings didn't go that away.

Your grammar was fine, but we would normally say it the way that I rephrased it.

After dohaving three massages at that blind massage shop, I thought that I should go to a hospital to see a doctor for a systemic check and treatment.

After seeing the nuclear magnetic resonance film Ithey took in that hospital, the doctor told me that my left shoulder had a rotator cuff injury.

The treatment plan he gave me was medium frequency physiotherapy and Chinese medicine fumigation.

Your was not grammatically wrong, but we would normally say "gave me" in this circumstance

I have been treated according to this plan five times up to today andso far and the symptoms have been alleviated a little.

Or we might say "the symptoms have lessened" or "the symptoms have been reduced somewhat", just to give you other common phrasings

The doctor said that there is no good method to cure this illness yet, and it can only be alleviatmanaged.

An illness is managed or treated, and pain is alleviated, but an illness is not alleviated (so far as I know).