Those Uni graduation glitches are very annoying. If not averse to using mods, NRaas DebugEnabler has a command that will grant a sim a degree in the major and with the GPA specified. I usually have my sims skip the graduation ceremony (unless I am strictly after photo opps) and run the DebugEnabler command on them once they get back home to give them the degree that I know they just earned. The sims get all of the same benefits, including the extra traits, they would have gotten the ceremony way. They even spin to their graduation robes for a few moments when the command is run.
There is generally no reason to uninstall and reinstall the game and EP/SPs unless one is recovering from hard drive failure or is changing the drive on which the game is installed. The installation concerns the Program Files, but those do not change over time or with usage unless a patch comes out and we're pretty sure we are done with those. What can impact things is the TS3 user game folder in Documents, as this is where one's saved games and all of the added content are.