No, they will not be doubled counted if you only entered them once under your business. This income will shows under your personal income totals because your self-employed business income is part of your personal income.
Also, the software will show your 1099 entry in other areas of the software because the software tries to save you time on entering forms, but it's not double entering it. However, it's great to check that your totals are calculating correctly which you can do from the Tax Summary and by previewing your Form 1040.
On the form, you'll see the net self-employed income (income minus expenses), on line 12, and you shouldn't see the income reported on other lines in the income section (lines 7 - 21). Follow the instructions below to double check: https://ttlc.intuit.com/replies/3302322