Frog, having them in with your chickens might be contributing to the runny noses and eyes. Baby goats are very suseptible (sp?) to allergies and irritants, much like small children. You can give childrens Benadryl, in the same dosage that you would give a small child,(follow dosing instructions on the label) and make sure that provide clean bedding and fresh water for them.
You need to make sure you listen to thier lungs and watch how they are breathing, if you notice that they are really working to breathe, or if they start sounding raspy or gurgly, you need to call the vet ASAP! Also, if they lay down and wont get up, stop eating or drinking or start feeling really warm to the touch, you need to call the vet, ASAP! Young goats decompensate quickly, and if they get pnuemonia, you can lose them in the span of a few hours, so keep an eye on them , keep them clean and dry and provide fresh water and bedding. Look up Tennesse Meat Goats on the web, they have lots of good information. Sorry the info is kinda scattered and the spelling is bad, had to take migraine meds and im a little goofy, but pm me if you think I can help, I have a guy I can call and he has been raising goats for over 25 years.