Gum oozing from cherry / plum trees can be due to a variety of causes, including infected wounds, infections (fungal, viral, bacterial), insect infestations (borers), or cold-damaged bark. It is most likely to be bacterial canker. If so, you should prune from the end of June to August to remove infected stems to health growth below.
The ivy won't have cause the oozing directly, but it is not a good idea to leave it there as it will reduce air circulation, restrict sunlight, etc..