Last night after I took a shower, I heard water still running and I saw that it was leaking from the bottom of the heater. I shut off the hot water and it still wouldn't stop, so I turned the water off for the whole house.
What should I do now?
It could be a loose fitting or the overpressure valve kicking in, but not likely.
The tanks in most water heaters eventually corrode, how fast depends on a number of factors, one of which is the amount and type of minerals in the water, as well as its acidity.
Once they do leak, repair is generally impractical and a new water heater is needed.
In any event, you need a plumber to check it out and solve the problem.