The CDC has provided some guidance regarding whether you can get the COVID-19 vaccine alongside other vaccinations, including:

If you get the COVID-19 vaccine first, wait at least 14 days before getting any other vaccine, including a flu or shingles vaccine. If you get another vaccine first, wait at least 14 days before getting your COVID-19 vaccine. However, if a two-dose COVID-19 vaccine is inadvertently given within 14 days of another vaccine, you do not need to reschedule your Dose 2 appointment; you should still complete the series on schedule.