Babies rub their eyes. It's just part of how they're made. I have tried everything I can to stop my 19-month-old from rubbing her eyes, but that's because she wears contact lenses and rubbing her eyes can lead to rubbing out her lenses and losing one, or, worse, causing her to damage her eye with the lense (these are rigid gas permeable lenses, btw).
The latter has actually never happened, and my daughter will rub her eyes quite hard and for an extended period of time if she's tired or the sun is in her eyes or her lense gets out of alignment or whatever, and she's been wearing contact lenses since she was 4 months old. The likelihood that your daughter is going to damage her eye by rubbing it is slim. The most probable cause of her harming her eye in this manner is if she has some sort of debris (sand, dirt, etc.) on her hands and reaches up to rub her eye and it gets into the eye. Also there's the possibility that she could maybe develop an eye infection if she's been in contact with someone who has recently had pink eye or some other highly communicable eye infection. Either way, the best way to prevent both of these from occurring is just to keep her hands as clean as possible. If you let her play in the sandbox, make sure you wash her hands as soon as she's done playing.
The eye is a pretty resilient organ, so unless you have a specific reason to be concerned that she's going to damage her eye (like, she has an eye condition or something), I don't think you really need to worry too much about it. If you want to prevent her from scratching her nose, the only thing we've found that works is just keeping nails clipped fairly frequently. It's not ideal because their nails grow so fast, but it should cut down on the scratching (my daughter has a scab on her nose for this exact reason right now).
Hope that helps some!
ETA: If you think that her eye-rubbing is way outside the norm (which I know can be hard to judge), then it might be worthwhile to bring it up at your next ped appointment. I suppose that excessive eye-rubbing could be the result of a more serious problem, and this website seems like it has some good points to look for if you're concerned about that.
ETA (again): I don't love this website as it's a disneyfamily.com site which I wouldn't consider to be the height of medical information, but they make some completely valid points about eyes and eye-rubbing in babies which I'd never really thought about before, namely that as your baby gets tired, the muscles surrounding their eyes also grow fatigued and rubbing the eyes will relieve the tension in and around the eye and eyelid (we've all done this before after working a long day, reading a lot, or spending too much time watching tv or on the computer). Additionally, the longer your eyes are open, the dryer they become and rubbing them somewhat stimulates tearing. Excessive eye-rubbing (as in, more than usual) can sometimes be a sign of a teething in some children.