Are fees for massage therapy by LMT referred by Physician an allowable medical expense deduction, if not covered by Insurance?

Yes. Medical expenses are the costs of diagnosis, cure, mitigation, treatment, or prevention of disease, and for the purpose of affecting any part or function of the body. These expenses include payments for medical services rendered by physicians, surgeons, dentists, and other medical practitioners. Since a doctor referred you to the Licensed Massage Therapist for a medical service (to alleviate neck, shoulder, back, and hip pain), your massage therapy is deductible. 

You can deduct on Schedule A (Form 1040) only the part of your medical and dental expenses that is more than 7.5% of your adjusted gross income (AGI), if you itemize your deductions. 

For more information, please see Publication 502.