I have been having some on again and off again smelly water from my bathroom sinks. This doesn't happen anywhere else in the house. What can the problem be?

Smell your overflow when you run the water. It stirs up bacteria and comes out through the overflow. That is probably what you are smelling. Every couple of months fill the sink up with water and a 1/4 cup of chlorine and with your hand, make a wave into the overflow. Do this about 4 times in an hour and it will smell better.

why do we get smelly water from our bathroom sink on the second floor.

Is it the water that smells? You may have a water quality issue. Check with your water provider if you have one. Otherwise see the post above that explains the problem.

Since you say that the smell doesn't come from the sink, and that you had issues with clogged pipes, we agree that your recent plumber's unclogging could be the prime suspect. Perhaps he was able to clear the clog to allow water to drain, but there might still be some leftover debris that is now starting to decay. We have heard that pouring a cup of household bleach down the drain may help kill the bacteria.