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New 1099 employee with Cobra insurance
For the first four months of the year, when you were an employee, the health insurance premiums were paid for with pre-tax money.  When you receive your W-2 at the end of the year, the amount in Box 1 of the W-2 will be reduced by the amount you paid for health insurance.  You can't deduct it on your tax return because it has already been deducted for you. Now that you are a 1099 independent contractor, you are self-employed and eligible for the self-employed health insurance deduction.  However, as you noted, the COBRA premiums are likely not eligible for this deduction, because the policy is in your old employer's name.  See this question for details, but keep in mind that there are conflicting answers on that question.