Hello and welcome to YT!!!!!
I would take her to the vet for the cut which may or may not be the reason why her eyes are tearing.
I wash the face everyday for the ones that have alot of tearing and also put cornstarch under the eyes, it seems to help the area stay dryer. Just make sure you don't get it in their eyes.
There are so many reasons that they could be tearing. Your vet is the first place to go, they can help you figure out why she is tearing so much.
Is she teething?? When they are teething or are stressed or ill, their eyes will tear.
What type of food is she eating?? Alot of foods have ingredients in it that do cause tearing. Putting her on a good holistic food can clear it up if that is that problem. Chicken Soup seems to be a great food for this.
Also giving distilled water instead of tap water can clear up the eyes.
Some dogs have overactive tearducts or the rims of the eyelids are not deep enough causing excessive tearing, your vet should be able to tell you if this is the cause.
Some dogs are genetically prone to have excessive tearing, it is in their genes and there is not much you can do about it if this is the case.
These are all some possible reasons why she is tearing so much. You have to figure out the cause first, otherwise any treatment you do may not work because you have not figured out why she is doing this. Like I said, going to the vet would be the first place to go and they can rule out what is not causing it.
Good luck with her!!!