I don't think it's possible for Epsom Salts to constipate you. They have a laxative effect.
How much Epsom Salt with water are you drinking? I usually do 1 and a half tablespoon in water at a time, which is a little more than called for. It does the trick. Maybe you should up the amount of Epsom Salts .
Very possibly some Stones clogging you up??? Lecithin Granules a tablespoon or so twice a day helps along with a coffee enema immediately the next day after the Flush.
Other than that, I don't know what it could be.
Try a Salt Water Flush to get things moving as well.