Play around with swallowing small pieces of ice. You can then work up to bigger pieces until you are swallowing some pieces much bigger than your pills. Ice is easy to swallow and will melt if it gets hung up some place. You will get to where you can swallow horse pill sized pieces of ice no problem.
Oh the shaking your head thing that X-ray talks about does seem to work for me too. I don’t very often but using the above I can swallow a whole hand full of pills at one go.