Cherry tree

Hello, I have never posted in a forum before so just bare with me. Last summer, I bought a cherry tree from my local green house, it looked fairly sturdy and healthy to me so I went ahead a brought it home. I planted it in my back yard which is very heavy in clay content. Throughout the summer i took good care of it and watered it every time the soil was dry since cherry trees do not like soil that is always moist, it seemed like it was growing just fine but it got to a point where it just didn’t grow anymore. I didn’t give up on it as it didn’t seem dead, there just wasn’t any more growth from the sprouts on the branches. Winter came along and I figured i’d wait for next spring to see if it was still alive or dead, spring came along and thankfully the old sprouts began to grow again. Until one week where the weather got extremely bad and froze off all the buds off, i was pretty upset about it as I looked at the tree, the inner layer of wood looked dark brown. I did some research and realized that the whole poor tree had been frozen to death. I was extremely bummed about it but i really had hope for my cherry tree to survive so i kept watering it as the weather got warmer and one day i looked down at the base and realized there was a tiny green shoot coming out of the base of the tree! Eventually more and more shoots started to come out but now i’m wondering if i should chop down the old tree for the new sprouts to grow bigger but there is a lot of them. This brings me to my question, Should I remove the old tree and cut off the smaller shoots? Or should i let them all grow out and see what happens?