Did this problem start when the water heater was installed?  How old is the house? Somewhere there is a partially clogged supply  line or an interconnect between hot and cold pipes. Good luck tracking this down!

My previous house was built in 1931 and had original plumbing.  The shower controls were in two sections. There was a mixer valve to control temperature and then separate on/off controls for the main shower head and the body sprays We had a problem when we went to replace the water heater and couldn't drain the heater after shutting off the cold water supply.  Turned out the shower mixer connected the hot and cold system and water was flowing through the valve; in our case sending warm water to the cold water feed at the bathroom sink.

If this is an electric WH, I'd say only your upper heating element is working, so due to convection, you only have a few gallons of 130degF water at the very top, and the rest of the tank is lukewarm. The scalding burst from your bathroom sink probably did not last very long, and just happened to draw-off a "slug" of very hot water, right off the top. Only one heating element is on at a time. The LOWER element does 90% of the work, heating the WHOLE tank, from the bottom up (convection). The UPPER element only kicks on WHILE you're using hot water, trying to compensate "on the fly" for the incoming cold water, to let you take a little bit longer shower.

Your lower element might be bad from the factory, or just not connected. Turn your circuit breaker OFF before checking, OR... just exercise your warranty. ;')

Run a faucet at full hot. Feel the pipe coming out of the water heater. Is it hot to the touch or Luke warm after 30 seconds?

Two days have passed since question was posted and Lyndee requested additional info to better answer. Another drive by.