After I flush my toilet the flapper won't go down and the toilet continues to run?

Thanks.

Did you look to see what is causing flapper not to go back down? Is the chain that holds that flapper stuck some place, or under the flapper? Is there something that is blocking it? Sometimes the chain is too long or too short. You can adjust that.

If you haven't done this already - turn off the water by the valve next to the toilet so that it doesn't run all the time. Check to see what is blocking or causing not it not to go down. If the flapper is down, but not making a good enough connection - you may need to get a new flapper.

The flapper is not a costly part. Installing it can be done fairly easy.

Sounds like your flapper linkage needs adjusting.
With the flapper seated the linkage wants to have 1/4" of play. Too much play and the flapper doesn't get pulled back enough giving you a short flush. Too tight and it lets water seep past the flapper. I adjust the chain by the link and if it needs fine tuning, I bend the flush lever rod a bit until I have the desired play in the linkage. One more thing about a flapper. you will see where the old flapper hooks onto the base of the white overflow tube. On a older type with no hooks the flapper has a ring that slips down over the overflow tube to the seat,(see image). If your tank has hooks, take a sharp knife or scissors and cut the neoprene ring off on the marks provided and hook the flapper on the hooks. Leaving the ring on will interfere with the flush. The water level in your tank should be 3/8 to 1/2" below the top of the overflow tube when the tank's filled. And the little tube wants to run from the ballcock and connect to the white overflow tube.. Good luck, Tom