A 1099 is a report of income that may be sent to you by certain customers or clients. You include the income on your tax return but you don't "file" it yourself. (If, in the course of your business, you pay a client or vendor or subcontractor more than $600, you may be required to issue them a 1099, but you do this at the end of the year (after Dec 31 and before Jan 31).
You file one tax return for the whole year. This will be a form 1040, and if you have certain kinds of small businesses, you might also include a schedule C to report business income and expenses. But you only do this once for the whole year.
What you need to do is make estimated tax payments, they are due April 15, June 15, September 15, and January 15, which covers taxes due on the previous quarter's income. You can make the payments directly at www.irs.gov/payments. For help estimating how much those payments should be, you can use form 1040-ES, or various accounting web sites or business accounting software like Quickbooks.
