In my opinion, coughing is much worse than sneezing. Sneezing is often environmental. I have never in my life heard a chicken cough. If I did, I would probably euthanize it. If you get antibiotics, you are treating it blindly and it may be viral and not treatable with antibiotics. The hardest thing for a new chicken owner to understand is that even if the bird seems to recover, most of these viral diseases are herpes types, which means they will now carry the disease for life and can always infect others. If these are your first chickens, you treat them and you ever add more to the flock, the new ones will probably contract what the original ones have. This is such a hard fact of life to learn and I hate that you are having to deal with illness already. Yes, stress can bring out symptoms of a disease the birds already carry. A healthy bird will not begin coughing just because it's moved to a new location IMO. Sneezing can be from too much ammonia or dust or chemicals, like paint, gasoline, etc. Tylan can be found at almost every feedstore, if you choose to treat. Personally, I would leave them alone and see if their immune systems fight it off. If not, then they are going to always be sick, on and off, even if they seem to get over this. I know some may disagree with me, but I'm used to that.