I don't know if you're using the same computer at home and at school, or two different machines. But, there may be a corruption problem for the character you're unable to select and log on with.
This character data is stored in a hidden data folder outside of the main RoM game folder. If you're using Vista or Windows 7, you can find the RoM data folder inside C:\Users\{username}\Documents. If you cannot find (see) this folder, open Control Panel, and find the Folder Options applet. Use that, click on the View tab, then click the radio button next to Show Hidden Files and Folders, then Apply.
Open the RoM data folder, and look for a folder with the affected character's name. Delete it, then restart the game client and log into the character. The server will rebuild the character folder. This usually fixes the problem.
It's also possible that if you're using addons, one of them may be affecting that particular character. You may have to unload or uninstall your addons, then re-install them one by one to see which one is causing the issue.
Hope this helps.