could be happening, usually the sole problem is that the chain hooked to the outside lever is hanging up or caught and not allowing the flapper to seat so that the back tank can fill up with water. Flush the com and with the back off, see if the flapper is falling back down and shutting off the pipe at the bottom of the tank.
If you have that old fashion metal float on your equipment then when you put your hand in the water you are causing the float to rise higher due to your hand water displacement and forcing the float to shut off the water. If this is the case, have all new guts installed inside the tank. this is a task for a handyman and not necessary to spend the big bucks on a plumber.