You're choking because you're playing scared. You're playing scared because you lack experience. In your mind you know what you should be capable of doing, but you don't believe it in your heart. It sounds cheesy, but it's true. So, the key for you is developing some emotion to go along with that talent. The good thing is that your body can lead the way in that area.
In practice, you kill people because you know them, you're comfortable with them. But, when it's a stranger, you tighten up. You don't know their tendencies and you don't know if they're going to lay you out if you try to drive on them. That sounds like me playing basketball in high school and being intimidated because I was a twig and I thought that I wasn't as good as the other guys (I only played pickup games).
As a pitcher, I didn't have that problem because I had proven myself TO MYSELF over and over again. I only got nervous in big games and I got nervous in quite a few college games as well until I got comfortable with the elevated level of play. You get better at learning tendencies faster and getting to maximum intensity faster.
Back to basketball. . . as I played more pickup games in college, I found that the best way for me to get over my timid play was to make the decision to be aggressive and then just go out and make some physical contact right away - hand check, post up, whatever. Don't concentrate on anything else except the first exchange. Just tell yourself, "Let's go" every time you handle the ball or your man gets the ball. Hell, I even smile a little when I think it and nothing pisses someone off more than you smirking at them like they aren't shit.
Find some pickup game at an outdoor court or at the Y. Play as many unfamiliar people as possible. Play big guys - older guys. I play at a YMCA, my community center, and at a neighborhood houses center in one of the worst areas of town. I'm never the best player. Sometimes, I may even be the worst. But, when I feel nervous, I just get inside and start banging and before you know it, I'm just playing.
Remember, when you start pushing on someone, the guy you're checking will try to pick up his intensity. He may even beat you on the first play or two. So you go beat? Just think, "No more of that shit," file the information away, and pick up the intensity. You won't ever win by shutting down and watching. You win by dialing it up every time and sticking your nose it the middle of it. The next time he goes for the same move, you can jump it. If you don't jump fast enough, believe me, you'll jump faster the next time.
Then, you go at him again and ramp it up a little more and make some more contact. Eventually, you'll be comfortable with contact and, more importantly, the intensity level around you because right now you're reacting instead of acting on your environment. You're watching instead of putting yourself in the middle of the action. You're scared.
Don't be. Stick you nose in it. Get bumped around. Get knocked on your ass. Get right back into it. You're not going to get shot or knifed in there. The worst thing that can happen is that you get beat or get flattened. Throw an elbow, lay up on your guy, hand check, but just get comfortable with touching someone and being in close proximity to someone who's intensity is ramped up to beat you. Don't be intimidated by aggression. Just keep ramping up your own intensity to match. You may find that the only way you can cope initially is to play pissed off. So, get pissed, get anything, but don't get passive. The more aggressive player almost always wins. If you foul out a couple times, don't worry about it. You will have contributed more in the time you were in there than an entire game of passive, timid play.
In basketball, there are many ways to contribute, many of which you can do well even if you're timid on the offensive side of the ball (fine motor ability goes to hell when you're inexperienced). When all else fails, just concentrate on defense, grabbing boards, and passing and leave the scoring to the other guys. BANGING AROUND FOR BOARDS IS ABSOLUTELY THE BEST WAY TO GET COMFORTABLE WITH NEW BODIES FLYING AROUND YOU. Get in there and fight every time. Jump as high as you can and rip the ball down as hard as you can every time. Be Dennis Rodman.
When you've gotten comfortable banging around with people, your scoring will come. Once you've settled down, the desire will build up and suddenly you'll be calling for the ball because that guy on your back will have just become another body that you've grown accustomed to and whose intensity you match or surpass. You'll start worrying less and less about what he's doing and you'll start concentrating more on exerting your will on him.
When you start getting comfortable enough to shoot, you're still going to lay some serious bricks. Relaxing while shooting (along with ball-handling for the point) is probably the toughest thing to do. You have to keep shooting - be sure to use your best moves right away to develop some flow in your game. Don't abandon them if they don't fall, keep using them until you get your range. Then, move on to other things. Eventually, you'll notice that you're relaxed when you go up for the shot. At that point, you'll be completely in the game, just worrying about playing and making adjustments. Then, it gets fun again. And, when it's fun, you'll really start to develop your skills and start pushing what you do in games compared to practice.
It's going to take time, but it will happen. Don't get discouraged. Get pissed. Pick up the intensity. Dial up your aggression. Just rebound and play D like a madman!