No, you should not deduct the same expense twice on your tax return.
You can deduct medical insurance as a business expense if:
The policy must be in your name or the business name
Your deduction for self-employed health insurance is limited to net income on your Schedule C less the deductible part of your self-employment tax (Form 1040 line 29), less contributions to a qualified retirement plan (TurboTax will do the math for you)
If you received a subsidy or premium tax credit to purchase a health insurance plan in the Health Insurance Marketplace through the Affordable Care Act, any advanced-payment subsidy that lowered the cost of your health insurance premiums cannot be claimed as a tax deduction. However, the money you paid out of your own pocket for your premiums might be tax deductible.
You can't include premiums for any month you were also eligible to participate in any subsidized health plan maintained by your employer or your spouse’s employer.
However, payments for those months are deductible on Schedule A if you itemize deductions
