One more suggestion...
Do a few sets of decline bench press. It doesn't have to be too heavy. Just "feel" how the bar path is kind of low on your chest. "Feel" how your elbows have to be lined up directly under your wrists. "Feel" the way that you are pressing the bar towards your feet, instead of just straight up. Almost like your pushing the bar along your belly. "Feel" how hard your upper back is working to keep your elbows in place, so the bar just doesn't fall backwards onto your face. Press towards your feet, keep the elbows under the wrists, forearms vertical.
Now go to the flat bench and do some close grip bench presses. Nothing crazy close, maybe 1 finger on the smooth, or right on the edge on the inside of the knurling. Focus on tucking your elbows on the descent, and touch a little low on your chest. On the way up keep your elbows tucked, keep the bar low on your chest, and think about pushing the bar towards your feet.
You should feel like your pushing the bar up and towards your belly. Keep the elbows tucked, and the bar path low over your chest. The range of motion should feel long, and your should really be able to feel it in your tri's. It will feel like you are pushing the bar at an angle, but in reality it will just be going straight up. Your triceps will have to work.
Sometimes you see people benching, and their chest/shoulders are stronger than their triceps. As they press, the bar drifts up, the wrists get cocked, and the elbows end up in front wrists. If you started on machines, it's possible you are now using a lot of chest and delt and not enough tricep when you bench.