The gumming can be caused by physical damage but I think in this case it is probably caused by bacterial canker. You can cut out the cankers and I think that is what you want to try doing initially. Long term you may want to look at planting cherries that have some resistance to the disease if it turns out to be common in your area. If you’re ordering a tree now I would choose one with resistance to canker.
Another thread talks about canker in detail. Look at the link to the post here:
I would look at that post then read the links in the post then finally review the other posts in the thread. That should give you a good foundation on how to deal with the issue and what would be the best course of action for you personally.