I own my own company and I received money from companies in other countries. None of them issued 1099's to me. I reported the income on my quarterly taxes as well as my deductions. When reporting it on my Federal Tax returrn do I include the deductions I paid that I claimed on my quarterly taxes? Or would that be double claiming?

Your quarterly tax return (Form 1040-ES) is an estimate of your tax liability used to determine how much you should pay to stay current in your tax payable status.

Since it is an estimate, the deductions used in making that estimate can be claimed again in your final annual tax return.

In other words, your annual tax return is the one that counts as being the return of record.