I do not have either cold or hot water from my tap in the kitchen and the one in the bathroom. The shower and the tub both have water but these two have nothing .... possibly an airlock? tried my thumb over it but heard that if your tank has a check valve or something like that that this method will not work? Also don't think I can get a good seal from my thumb over the nozzle? Tried blocking in the water underneath sink and opening it again with no luck. I had just finished draining my hot water tank and flushing the sludge out of it and don't think we purged the air correctly? Now no hot or cold from only those locations ....
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.
Sometimes the junk in the bottom of the tank will mix with the water and flow to the smaller shut off valves and plug them. Take the line off the discharge end of the valve and see if water comes out when the valve opens. If no water comes out or the flow is reduced, you may need to replace the valve or if you are not sure you can do this, you may need to call a plumber. Also, the other guys Ideas are worth trying since anything could be a possible fix. Flushing out hot water tanks almost always causes a lot of water flow problems in valves and small piping.
I just fixed this problem by turning off main, opening all faucets and tubs, letting all run dry, turning on the main, letting all water run a minute, then closing each faucet and tub one by one. By the time I got to the one that hadn’t worked, water was shooting out like normal. Must have been an air bubble.
I just fixed a similar problem using a technique that our plumber used when we had this problem a few years ago. He borrowed our Vax Wet vacuum cleaner, sealed the tube to the tap and then sucked the air lock through. You need to get a fairly good seal - we used a wet cloth, clamped using hands. It took a minute or two to suck the air through.