If you chose to file as a Single Member LLC, then no, you do not issue your self a Form 1099-MISC. A Single Member LLC files a Schedule C and the income is reported on your Form 1040.
If a single-member LLC does not elect to be treated as a corporation, the LLC is a "disregarded entity," and the LLC's activities should be reflected on its owner's federal tax return. If the owner is an individual, the activities of the LLC will generally be reflected on: See the following IRS article: https://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Single-Member-Limited-Liability-Comp...
