OK, so sorry to hear that your nose is broken, which would give rise to a lot of trouble and inconvenience to your daily life. So, it is normal for your glasses to slip down your broken nose. Anyway, I could not figure out a better way, except contact lenses. With contact lenses, you would be able to have better vision and be free from those glasses. Hope you find this useful. If possible, just try to fix your broken nose.
You could just adjust the position of the nose pad of the eyeglasses. If you still feel not comfortable when you wear the eyeglasses, you could just wear the contact lenses which will be convenient for you. At the same time, you will get the right vision when seeing things. You should treat the broken nose as soon as possible.