My dog got bit :-( what to do??

Sorry if this is in the wrong group!! I need some help!! My dog is about 40lbs, she’s on the smaller side, and my mom’s Great Dane bit her. There’s only one puncture, but it was pretty deep. My mom said not to take her to the vet and that she’d be fine, but I think I’m gonna make an appointment anyways. It’s a nice sized wound near her right shoulder. I don’t know how deep it is, but I could see inside when I used my flashlight. This picture was from about two days ago, it’s the best picture I could get. I’ve been putting antibiotic ointment on it, but it seems like it’s still leaking a little bit, and it looks a bit irritated today. My dog is acting fine at the moment, no signs of a fever or anything, but do you guys think I should take her to the vet just in case? I don’t want it to get infected.