Can I deduct gym membership fees, and personal training costs as medical expenses?

No.  IRS regulations are clear that excercise costs are not deductible even if medically recommended.  

Some weight loss expenses are deductible.  Your gym membership is not deductible, but if you pay extra for specific weight loss activities, that might be deductible.  Whether you could justify your trainer as a specific weight loss activity instead of for general health, strength and flexibility might depend on the trainers qualifications and specific activities you engage in.  

Weight-Loss Program

You can include in medical expenses amounts you pay to lose weight if it is a treatment for a specific disease diagnosed by a physician (such as obesity, hypertension, or heart disease). This includes fees you pay for membership in a weight reduction group as well as fees for attendance at periodic meetings. You can't include membership dues in a gym, health club, or spa as medical expenses, but you can include separate fees charged there for weight loss activities.

You can't include the cost of diet food or beverages in medical expenses because the diet food and beverages substitute for what is normally consumed to satisfy nutritional needs. You can include the cost of special food in medical expenses only if:

The amount you can include in medical expenses is limited to the amount by which the cost of the special food exceeds the cost of a normal diet

@James-M  even if deductible, you won't get any tax benefit unless your itemized deductions exceed your standard deduction. in addition, qualified medical expenses are only deductible to the extent they exceed 7.5% of your adjusted gross income.

however if you have an HSA

You can receive tax-free distributions from your HSA to pay or be reimbursed for qualified medical expenses you incur after you establish the HSA. If you receive distributions for other reasons, the amount you withdraw will be subject to income tax and may be subject to an additional 20% tax.

Qualified medical expenses are those expenses that would generally qualify for the medical and dental expenses deduction. You can’t deduct qualified medical expenses as an itemized deduction on Schedule A (Form 1040) that are equal to the tax-free distribution from your HSA.

You’ll want to keep all your receipts, especially for gym memberships and personal training fees. The IRS allows you to deduct those if they're prescribed by a doctor for a specific health issue, which it sounds like you’ve got covered.

I went through something similar last year after my doctor recommended regular workouts. I found this great fitness business software that helped me keep track of my sessions and manage my membership costs better. It really made things easier! Also, don’t forget to check if your state has any specific deductions or credits for fitness-related expenses—sometimes they do! It’s worth looking into.