No water from certain taps
Without being there to see the problem its hard to give a sure fire "here's the problem answer" but Tubs do not have aerators. I'm assuming your sinks both do.

This coupled with the note that you indicated you just drained sludge from your hot water tank leads me to believe you are on well water or hard water, or at least, potentially untreated water.

I would suggest removing the aerator on whichever sink is easy to remove on and then try it. I have seen in my mother in laws house an aerator so plugged that it didn't even allow a drop of water out. Since you disturbed sediment in the tank, it likely set larger pieces free and thus clogged the aerator.

You can usually separate the screens in an aerator and clean them and the plastic diverter/distributor parts and reuse them. Eventually its easier to just replace them, they can be had at any local hardware store for a nominal price. Bring yours with you if this is the case because they have different thread types and sizes and depth.

In the future, when you clear sludge from the tank, run the tub for a good while before trying the sinks. Also, it is possible to plug toilet lines with sludge as well.