Video of me swimming. Yes, I am horrible

Couple of things that could be pretty easy to address.  Note the position of your right shoulder and hip and how much rotation there is (because you are breathing on that side).  Then look at how little your left side comes out in comparison.  You need more rotation especially to your left.

When you get this rotation going better, you will find it easier to get your elbow high during the overhead recovery.  When the body is rolled and the elbow is high, lead your arm forward with the elbow in front (not the hand) until you get at least to around your head.

This should make things more efficient, but it should also make things much easier on your shoulders.

ETA, I just saw the second video down.  Bend that right arm in recovery and bring your hand right past your ear (instead of swinging it out to the "long way").  Google the finger tip drill and maybe the zipper drill, they will help immensely.

Couple of quick things before heading to bed, you need to work on your rotation, and your catch.  Search for a few videos showing proper technique and compare.  As of right now, your stroke is fairly inefficient, but can be fixed easily.

See the Endless Pool ad to the right of this forum page (not the thread page)? Notice the high elbows on the dude swimming? Instead of the hand travelling out to the side in an arcing motion, the hand moves in a much more linear (and efficient) manner to the head.

I think it is supposed to enter about a foot in front of your head, the final extension should be under water, but if you do it too soon it will not be beneficial.  As others have said on another thread, hand should enter at a 45 degree angle in front of your head.