Are annuity fees considered investment expenses? This is the monthly fee that my annuity charges me.

For purposes of your tax return, the monthly internal charges of an annuity are not considered investment expense. 

Investment expense (for tax purposes) would include things like custodial fees and investment advisor fees.  These are not presently deductible on the federal return, but are deductible in a few states. 

Fees for annuities, internal fees for mutual funds (sometimes called "12-b-1 fees") and commissions are not expenses for this purpose, but do reduce the gain that you may see on your investment.