What can I do for my sick pets?

My dog, I don't even know what to call it, but it's like he's coughing/wheezing with his mouth closed. It's not constant, but he goes into these "coughing fits" a few times a day that last about half an hour.

My cat seems to have a cold. She is sneezing almost constantly. She has been more clingy and snuggly than usual.

I did not grow up with pets and our pets have never been noticeably sick in the 5 years we have had them. My husband has had several pets all his life and just told me to make sure they always have plenty of water and give them extra snuggles. I just feel like I need to do something to help them get better. They are my babies Is there anything I can do?

So far my other dog does not seem sick, anything I can do to keep it that way?