Your elbow is fine. The elbow out thing is a little blown out of proportion. As long as it's not crazy out so much that your extension is off-line and putting some side spin on the ball you're good.
Theory time: For people that aren't particularly accurate shooters but have good mechanics or have concentrated a lot on their mechanics, I think a common culprit is over-complicating the thought process. A lot of bad shooters, especially bad freethrow shooters, spend too much time trying to not miss the shot instead of trying to make the shot. To be a good shooter, you have to try and make the shot. By this I mean, surrender to your primal targeting instincts. All humans have evolved over thousands of years honing a primal targeting instinct. If you wanted some protein during prehistoric times, chances are you had to throw something at an animal to kill it. From throwing stones, sticks purposely used for hunting/throwing, spears, atlatls all the way up to bow and arrow and eventually firearms, the basic premise was the same: Locate target, throw projectile at target. Your brain is amazing at subconsciously calculating what you need to do to hit an object, think about how little you have to think about the next time you throw a rock at a tree or a beer can into the trash can.
Translating this to basketball: It's really simple. Locate your target (the rim) and throw the projectile (ball) at it. Now, when you locate the target, it's very important to refine that target to produce the most optimal result (i.e. a made basket), aka "aim small, miss small." If you focus on the front of the rim, chances are your misses will tend to miss short. Look at the back of the iron? You'll probably miss a little too long. You want to focus inside the rim, the center. You can't really see it most of the time but your brain is great at processing abstract thought so you can imagine where it is. Your brain will also help process the amount of arc needed to get over the front of the rim to hit that center, too. Every shot in a game is really unique (with the possible exception of the freethrow if you can locate the nail) so translating this "primal targeting instinct" to the court is integral to being able to hit shots from all over the floor. Everybody has sweet spots on the floor where they've done a lot of reps but without "primal targeting instinct" you're practically reduced to only your sweet spots and your "clutchness" can be greatly affected.
Bad free throw shooters (with good mechanics) are a great example of people that fail to do this. They are so concerned with keeping their elbow in, bending their knees perfectly, flicking that wrist and maintaining that all-important gooseneck in their follow through that they forget to do the most important part: Trying to actually make the freethrow. Instead, they try to not miss and it's a good recipe for getting "the yips."