I have a small cherry tree that has some glue leaking, think it might have a wound that I didn't notice before, probably from when it snowed in spring last year. There are also some yellow leaves on a branch.
It may not 'heal' at all - this is gummosis, which occurs for various reasons and is common in cherry trees. Likely the cold weather caused a fracture in the trunk/bark and this is the result. Sometimes, bacteria invades the area and then the exudate gets very unpleasant smelling, by which time its usually too late to save the tree. At this stage, you might be able to prevent it getting worse though; this link https://www.gardeningknowhow.com/edible/fruits/fegen/what-is-gummosis.htm suggests stripping back the bark to healthy bark. Otherwise, there is no treatment I'm afraid.
Actually, this is bacterial canker which can affect cherries. That’s what we call it in the UK. There is no cure. Further more, you need to get rid of the tree carefully and burnt it to destroy the bacteria. Otherwise it will affect other trees in the area, especially if you have plums or other cherries.