The former University of Texas quarterback was knocked out early in last week's 37-21 loss to Alabama in the BCS championship game. A hard tackle pinched a nerve and caused McCoy's throwing arm to go numb.
McCoy was announced Thursday as the winner of the Manning Award as the nation's best college quarterback. In a conference call with reporters, McCoy said he met with sports doctor James Andrews in Birmingham, Ala., on Monday and was told he'll have a full recovery without surgery.
"He basically told me I would be fine with two weeks of rehab," McCoy said.
"I certainly expect to go and do things at the combine," McCoy said. "I'm doing much better now."
NFL teams will be interested in how quickly McCoy recovers. When he was a freshman in 2006, a pinched nerve in his throwing shoulder knocked him out of a loss at Kansas State and affected him two weeks later in a defeat to Texas A&M.
McCoy said Andrews assured him the latest injury doesn't give him a higher risk of having it happen again, but he didn't want to speculate on where he might be taken in the April draft.
McCoy has signed with an agent, David Dunn, and was in California to start his rehabilitation. McCoy said his right arm is getting stronger every day.
McCoy, whose 45 career wins as a starting quarterback are an NCAA record, said he was hurt by some suggestions that he should have tried to return to the game. Freshman Garrett Gilbert played the rest of the game and led a second-half comeback that fell short late in the fourth quarter.
"That's bad for somebody to say. That frustrates me," McCoy said. "That's just people talking. If the rest of my body was numb and my right arm was healthy, I would have been out there playing. It took away what I do, and that's throwing the ball."
McCoy also talked about his Monday night engagement to girlfriend Rachel Glandorf. McCoy proposed on the 50-yard line at Royal-Texas Memorial Stadium.
McCoy said he designed the engagement ring. He bought it before the bowl game and kept it secret from everyone except his mother. He didn't reveal the carat weight of the diamonds.
After receiving a good medical report and signing with his agent, McCoy said, the time was right to propose. He had "Will You Marry Me" written on the stadium's giant high-definition scoreboard screen for the big moment and dropped to his knee to ask Glandorf.
"Rachel and I have been dating for a long time," McCoy said. "As I was going off to get ready for the next phase of my life, I wanted her to be a part of it."
Copyright 2010 by The Associated Press