NOTE FOR 2018 AND LATER (added 3/10/19): The new tax law eliminates all itemized deductions that are subject to the 2% of AGI limitation, including job-related mileage and other job related expenses, for 2018 through 2025. That means that a W-2 employee cannot claim any deduction for job-related mileage.
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Original answer for 2015 tax returns follows.
It sounds like this is for a job where you are an employee, and you get a W-2. Also, if I understand correctly, the car allowance is a fixed amount per month. It's not based on your mileage or actual expenses, and you don't file an expense report or account to your employer in any way for the usage of your personal car. Since you say that the car allowance is taxed, I assume it's included in your paychecks, and in the wages in box 1 of your W-2.
If my understanding of the situation is correct, as outlined above, then the car allowance is just extra pay, regardless of what your employer calls it. That means you can claim your actual mileage as a job-related expense. This might or might not reduce your tax or increase your refund. Job-related expenses are a miscellaneous itemized deduction subject to the 2% of AGI limitation. That means that 2% of your Adjusted Gross Income (AGI) is subtracted from your total miscellaneous itemized deductions. Only the remaining amount is deductible. In addition, the deduction will not have any tax benefit unless your total itemized deductions are more than your standard deduction.
BUT - You appear to be using TurboTax Home & Business, which suggests that you might be self-employed. If the car allowance is related to self-employment income, the situation is entirely different. If this is the case, please provide more details about who is paying the car allowance to you, and how it is taxed.
