buster, I get the same thing sometimes when I start out with too heavy/not enough warmup. Its counterintuitive that a muscle that doesn't even engage while doing a bench press would burn after doing a bench press, right? For me, its not actually the post delt, its the infraspinatus, which is right underneath the post delt and covers the scapula(shoulder blade). The insertion of the infraspinatus is the greater tubercle of the humerus, which means the tendon of the infra runs deep(meaning opposite of superficial) to the post delt. I was stressing that tendon. I was baffled by this for a bit myself. When doing benches, your 'rotator cuff,' which is actually just 4 muscles(supraspinatus, infraspinatus, teres minor, and subscapularis) have to strain hard to retain the head of the humerus in the shoulder socket. This straining is causing a slight burn in the infra. My shoudlers are my strongest body parts, and I still get this same burn sometimes when I get a bit overzealous and go too heavy too fast. You're headed for a rotator cuff injury if you don't take time to incorporate rotator cuff strengthening exercises into your workout.
My fix for this problem is that I do 2 warmup sets before going heavy. I throw a 25 on both sides, do 20 reps just to get the muscles movin, then streeeeeeeeeeeetch.. Then throw on another 45 plate on both sides, do about 15 or 16 or so and then streeeetch like hell again. During these stretches you should not only stretch the chest, but also the rear shoulder area. Then go hard at whatever rep/weight level I'm going for that day. If you work up to the weight it will decrease the burn. A good exercise to strengthen the infraspinatus is upright rows with elbows up at shoulder level as opposed to down(you will want to use a wide grip.. this will isolate the muscles of the shoulder as opposed to isolating the lats.) Of course, use lower weight compared to what you would normally do for the lat version of the row, and you want to do a higher number of reps per set, like 15-18 or therabouts, and each rep should be slow and controlled with a deep stretch in between each one.. The bar should go from as far away as your arms will stretch out all way in to your sternum for EACH rep. The rotator cuff muscles, by nature, are endurance muscles, work them as such. Take it easy on the heavy ass bench presses until you get the complementary muscles which make bench press possible strengthened. For a few weeks work on this while doing less weight/higher reps on your benches. Your other chest exercises should be unaffected by the infra issue.