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No. I would not use it on the pup. You can wash the eye with warm saline or water tonight very gently to remove the goo. Then you should see your vet tomorrow if it doesn't look like it's improving.
Because you are seeing colored mucus, I am guessing that it's an eye infection. If it is, you need the vet to diagnose it and give you appropriate meds for a puppy.
Let me know if you have more questions.
You are correct. Washing the eye will not clear up an infection but it will give her some comfort until you see the vet.
Without looking at it, I can't be sure about what is wrong with her. If you see the vet tomorrow, there is a good chance that you can save her sight.
Let me know if you still have questions.