Colitis in Dogs
check this information out on colitis sounds to me to be the problem and ibd and colitis are very similar in nature it is an inflamed bowel.
I would not feed a poultry especially with an allergy dog. i have an allergy dog and an ibd dog both are yorkies. I know alot about this stuff. Constipation has never been an issue more vomitting as my dog has issues in small intestines sounds like yours has issues in large intestines it is getting stopped up down their due to diet.
Many dogs that have allergies also have IBD - ibd is a food intolerance which is different than food allergy. It is more tied to inflammation of the GI tract. If you think about it if something gets inflamed it can get stuck or it can be so inflamed something goes straight through without being processed.
If this were my dog I would personally do the venison and sweet potato for 12 weeks and supplement with the coconut oil as it is a natural antibacterial and antifungal and it is a good natural oil that can help move things along. It is excellent for allergy dogs too as my allergy dog takes it and when i stopped for a year she got a staph infection so back on it.
I would also get lactulose and if your dog has an episode of constipation i would use the lactulose as i know it works well for liver shunt dogs who have a hard time releasing toxins.
It seems the mylicon is more for gas than constipation