After a lengthy reply was lost, I'll be brief. You're using your flight isntructor's certificate, not just your own...why are you asking here, when you should be asking him or her?
How do you know the work has been done properly? Because someone told you? Can you recognize a proper repair? You should, if you're going to accept responsibility for the work...and you are, if you fly it.
The mechanic can approve the work for return to service, but he cannot return it to service. You do that. You do that by flying the airplane. In so doing, you take full repsonbility for the safe and airworthy condition of the aircraft. That particularly includes the work that's been done.
So as a student pilot you're asking an anonymous web board if you should fly this aircraft, instead of your instructor? What makes this flight so urgent?
How do you know additional damage hasn't occured? If the linkage was broken as the result of shimmy or vibration, common damage includes engine mounts, vertical stab attach brackets, firewall damge, and rudder linkage.
You'd surely hate to have a stuck fully deflected rudder as you flare or land in a crosswind, or to have to fly a go-around like that for a pattern to landing, because of unseen damage. It can occur, trust me.
How about you ask your instructor, first? Do you know what maintenance entries to look for? Without all the signatures and paperwork done the airworthiness certificate is invalidated. There's more to the issue than you may think, so don't rush off and do something without your instructor and knowing everything you need to know to do it right.
ASquared noted the possibility of you needing a private pilot certificate. This is the case if the aircraft "has been maintained, rebuilt, or altered in a manner that may have appreciably changed its flight characteristics or substantially affected its operation in flight." That may, or may not be the case here, and without seeing the aircraft or knowing the specific application, it's hard to say.
The fact that you own the aircraft is irrelevant, and shouldn't be a part of the discussion.
One step at a time, grasshopper.