You need to do 2 things with your grip. You are probably pushing the heel of your hand too far into the grip or you are too much heel to the right on the grip (rh archer). Grip the bow with a feeling that your hand is wrapped "around the bow". Really get a hold of the grip on the side. I mean white knuckle the thing. You must get your hand around the side of the grip and hold it tightly. This will inturn put some bend in your bow arm and get that string away from your arm. You will also notice that you will get cleaner arrow flight and eliminate those left arrows if you are gripping properly. If you can get a copy of "hitting them like Howard Hill" it can be very beneficial. I was taught by that book and video and a great gentleman named Max Drumb the Hill style of shooting when I was 16 YOA. Max was personally instructed by Jerry Hill. I have tried many other ways to shoot a longbow, but the Hill method I always return to as the most accurate for hunting situations with a straight limbed bow. One other point is to close your stance and point your left shoulder (right handed archer) at your intended target. Get up to the target close. Draw the bow to full draw and anchor with your eyes closed and then look at where the arrow is pointed. Self bows and longbows are not center shot. The arrow more than likely will be pointed to the left. Adjust you feet and point your shoulder at the target until you can pull up with your eyes closed and the arrow is pointed at the target directly under the spot you want to hit. Memorize this stance. This will give you a standard to go by. With practice you can adapt from this standard to shoot in more awkward hunting positions. Bend your knee, front on downhill, rear on uphill, keep torso erect and cant head at the neck, right and forward (RH Archer). Gave you some things to try.
Longbows and Short Shots,
Jeff Schulz