Yes hamsters can pick up human viruses such as the cold virus.
You can read about cold care here
http://www.hamsterific.com/IllnessGuide.cfm#Colds
http://www.hamsterhideout.com/ailments.html#colds
http://www.pgaa.com/burrow/general/hamster.html#ailments
Best option may be antibiotics from the vet but the above sites have info on home care and housing conditions etc for a hamster with a cold.
Hope this helps you!
Pet Health Care, Rescue,Train,Breed
30+yrs pet vet care & nursing, rescue, behavior & training, responsible breeding, small animal care