After flushing my toilet, then it fills up. My toilet sounds like its running

Make sure the float shuts the water off 1" below the overflow. Make sure the flapper is seating properly, check to see if the chain is caught under it. Put some food coloring in the tank and see if the bowl colors. If it does, the flapper is not sealing.

By running are you saying it repeatedly refills the tank or do you hear water trickling all of the time/maybe both are true

it always sounds like water is running
More details please! What, exactly, do you mean by "running"? Does it refill? Does it seep out into then bowl? Give us something to work with here. Regards, bTom