I turned off the hot water and cold water valve to replace my aerator. Then when I turned on the cold water valve everything was fine. But as soon as I started to turn on my hot water valve from under the sink, the water started dripping out of the faucet aerator slowly at first and then when I kept on turning the hot water valve on more it started dripping faster... uh oh... please help me!! :(

Your hot water side of the faucet need a new gasket or simply replace the guts of the faucet, if your lucky you have a modular style which will make it very simple

Another possibility is that turning off the hot water valve and then back on loosened up some crud in the line which then lodged in the valve and interfered with it closing completely. This if more common in hot water lines than cold because water heaters tend to accumulate sediments that can get stirred up with pressure spikes (e.g. when water is turned off/on.

I have had this happen several times and have always been able to fix it by taking the faucet/valve apart and putting it back together after cleaning the parts. Make sure you leave the aerator off and flush the system before putting it back on since they also tend to get clogged by sediments.

Just a thought.

--John