First, there`s really no difference between a single member LLC and an individual. The LLC is what the IRS calls a "disregarded entity" for tax purposes, and reports its business income and expenses on a Schedule C just like a sole proprietor does.
So one or two 1099s won`t change the tax effect.
The question I have is whether you actually are an independent contractor. It`s hard to tell without knowing some more details, but if your situation is mis-classified, that could cause some problems.