Can just walking around in a public place like a library (no physical contact with people) cause you to catch any type of virus?

Very unlikely: Some viruses (and bacteria) are spread through the air, e.g. when people cough. However, almost all such infections require pretty close physical contact or at least coughing right in the face. The risk is very low from simply being in a public area. Be sure you are up to date on immunizations, including influenza vaccination once a year. Otherwise don't worry about this.