Former U.S. Open champ Johnny Miller has a good definition for choking, and it applies to all sports.
In golf, choking involves blowing a shot because you vary your normal swing in a pressure situation. To avoid choking, rely on your training.
Proper breathing helps prevent choking, and some players say yogi helps develop a calm state of mind for playing.
As both a player and a former caddie, I also saw "learned helplessness" come into play. You have a couple of bad experiences on a tough hole, and you start expecting "bad things to happen" when you play the hole. I play at a Jack Nicklaus-designed course, and after season one I worried about five "evil holes."
I would go out on the course on a quiet day, and spend about an hour hitting different shots from different places on the "evil holes." Just shooting around on the hole allows you to be more creative, and you can figure out what you should do. This season, one short, tight par 4 is still "resident evil," but I occasionally get a par on the former evil ones.
Do you have a pattern of how you blow the last two holes? Is there something you change up that hurts you (a la J. Miller's warning?) Pull a drive into the tree line, push a tee shot into a creek, hit a line-drive 6-iron approach that goes OB over the green? If you see patterns, work to break out of them.
For two years I would block out my drive on the 17th hole at most any course. I played in a pro-am, and the pro told me that I didn't waggle my hands on the shots I blocked out. Again, I was varying my routine - to something bad - and missing shots because I was tensed up. This tip didn't put me on the Pro Tour, but it did cut down on misses on late-round drives.
You're on the golf team, and I'm a 25 HDCP. I'm sure you'll figure something out.
And, have fun when you play. (It's allowed!!)