Chest infections - can I pass on germs even if I don't develop a chest infection?

I'm going to visit My mum this weekend. Although I don't have a Chest Infection, there are two people at work that sit opposite me and next to me that have chest infections and are constantly coughing. My mum picks up chest infections very easily which wipes her out for weeks. Even though I haven't got a chest Infection, can I still carry the germ and pass it onto her?
Make sure that you use a hand sanitizer really good after you leave work that day. Take a really good hot shower before you go to your mom's and put on fresh clothes. It Wouldn't hurt to wear different shoes that you don't normally wear to work either. I can't think of any more precautions you could take.

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