Well, i do blieve in this i don't know if you do or other people do, but i blieve it's bad luck to have broken things around you.. I'd suggest you creat a new wand, as this is a magical object, i'd suggest you just get rid of the broken one and make a new one.
Personally, I don't think there would be a problem with fixing it and continuing to use it. After all, something that's repaired isn't broken anymore. You might want to be more careful with it moving forward though.
Fix it. You can add a little something magickal to the glue or use a charm on it.
Limit your impact on the environment and repair things rather than replace them.
Whenever you use that wand now it will a reminder of what happened. Its a nice way to remember all your past rituals by, if you use the same tools each time.
It will be a little different from other peoples because you broke it and fixed it. You put energy into both those things and to me that is a little bit magickal in itself.
A fixed item may have cracks, but those can be worked around. Wrap over the broken part with cord or write a charm or something similar to shore up the repair and wrap that around the broken area after fixing it.
There is nothing magical about a wand. It is merely a "pointer". I know many witches who have never had a wand. I have never had one. I know some Wiccans who use a wand, but merely as an extension to their own arm; for instance in drawing a protective circle around a work area. A wand is just a tool. Only Harry Potter uses a wand for magic; and he is fiction!