See if you can ask the nursery what the rootstock is. It might or might not produce a cherry that you would like for eating (many cherry rootstocks are crosses of different types of cherry), but it definitely won't be the cherry you wanted or any other cherry variety that is normally grown for fruit.

If someone around you has a cherry tree that you like, you could ask them for a couple of cuttings that you could try to graft onto your surviving rootstock.

I had the same thing happen to my super-dwarf apple - I did let the rootstock grow, then grafted a desirable apple onto it. (It took me a couple of tries, but I finally succeeded!)