It sounds like you may have a really strong let-down. If you've fed him laying down until now, it may not have been noticeable. Now that you are able to sit up, try leaning back when he first latches on and lean back for the first few minutes while the let-down is taking place. Then gravity isn't adding so much to the forceful let-down. It sounds like he may just be getting overwhelmed by the amount of milk at first and is having trouble swallowing it fast enough if he is coughing and burping a lot. Good luck, and I hope that helps a little!
Sarah , wife to Tyson :, SAHM to three little boys and a baby girl on the way!