No you do not need to file a form 8833 for that income. According to this IRS FAQ item 5 under the "Exceptions" paragraph states there is an exception to filing the form 8833 if "The payments or items of income that are otherwise required to be disclosed total no more than $10,000." Also, the form 8833 is filed to report an exclusion of income or lower tax based on a treaty. In your case you are including income to be taxed as US income.
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