Hi Tnice4ever:
Welcome to AMHD. Are you on city/town sewer or septic??
It appears that you have a clogged drain line

The question is if the branch drain picking up utility tub and kitchen sink is clogged or the whole house is clogged.. (or if septic needs to be pumped?) ??
Need to check obvious first!! Here, check if flushing toilets, running sinks and tubs/showers cause water to back up into utility sink. Run water/flush toilets..see what happens. If nothing, then just confirm kitchen sink causes backed up drain and be prepared to rent an electric snake (see pic.). If yes...need to locate the main drain cleanout...or check to see when last time septic was pumped. Let me know your situation...Mark