can chickens catch a cold from another type of animal?

You can look at this common poultry diseases website if you want until someone answers specifically:

It tells you species affected and has handy diagnosis charts at the bottom of the page.

http://edis.ifas.ufl.edu/ps044

Oh and medicated chick feed is just for coccidiosis, not sneezing.
If you have already started antibiotics, I would finish the course so you don't end up with resistant organisms. Although, if it is a virus, the antibiotics won't help.

 

Most dieases are species specific. There are a few that can jump the species barrier but there are not many.

The most common cause for birds to sneeze is dusty conditions or feed but be on the lookout for other symptoms such as bubbles in the front corners of the eyes, labored breathing or raspy breathing.

The best time to check the breathing is at night while they are asleep and the world is quiet and the humidity is up. If you can hear them breathing from a few feet there could be problems.