I have a job on Shabbos of working with a special needs boy, and I get paid per hour by the government. Occasionally, (when he has an off שבת or by ימים טובים I work with him during the week as well, but on most weeks, I only work with him on שבת. After שבת, I fill out a timesheet, and on the timesheet I have to write what goals I worked with him over שבת. Is that job of filling out that sheet with the goals considered part of the job, so that we can say I get paid בהבלאה, of this job of filling out the goals

Shalom U'vracha, Yes. You can consider the little work that you do after Shabbos part of the job and it would be considered "behavlaa" (see Shemirat Shabbat K'ehilchita 28:72-73). By the way, there are other reasons to be lenient in this case. It is surely a mitzvah to help this boy (see Shulchan Aruch 306:5, Mishna Brura 24, /shmirat Shabbat Kehilchata 28--comment 155). If you originally agreed that you will work on the days that he's home then your monthly payment includes the weekdays (see Shemirat Shabbat Kehilchita 28:64). All the best!