Its not that big of a deal, really...
Its not like you'll remember your jet years down the road...
like 78-546 (AK, 1994-1996) or
84-019 (Spangdahalem, 1997-1998) or
78-568 (Tyndall 1999-2002)...
You need to get to know your crew chief...buy him beers and/or steaks, and take a personal interest in both him/her and your steed. A good crew chief doesn't buy his Dining Inn ticket or his Christmas Party ticket if your CC allows you to take care of those things. Squadron T-shirts and patches are also usually appreciated...
Take an interest in your jet. If you can fly it regularly, you WILL get to know some of its habits and can sometimes recognize problems before they get big (part of the reason for the whole program in F15 squadrons...) I flew 84-019 as Mission Commander several times during OSW and had some of my flight members and best friends flying with me on those missions and I still remember how proud I was to have my bros, my jet, and my squadron out there at the tip of the spear for a few hours.
Again--way to go. You can be CEO of a corporation, or a big league ball player, or a Hollywood celebrity. However, as a soldier with your name on a piece of war fighting equipment you have earned something that nobody can buy, but rather has to be earned. You have a right to be proud...