Characters are completely stored on the server, a client crash can't make you lose them. However, a reinstall is probably not necessary; in the launcher options, you can force a full file check. That should examine every file and redownload any that are corrupt.
On rare occasions, that doesn't work, in which case you have two options:
1) If you can see the crash before it goes away, it may tell you what file it's crashing in. You can then delete that file and it will automatically redownload it.
2) If not, then yes, you'll need to reinstall.