K.P.
My son is 18 months and when he gets a cold it literally lasts for a month. I asked my pediatrician last year about it and his answer made a lot of sense. Essentially, all of the things that adults do to ward-off or treat a cold are "off limits" to babies. His "rule of thumb" is that it will take a baby twice as long to recover from a cold.
I asked about allergies for the same reason at about the same age- essentially the doctor told me that he was too young to determine whether or not he had them, but that we should treat his environment as though he did-
1. Nothing "perfumed"- including us!
2. Humidifier in the room
3. Dust/vaccuum daily
4. Warm baths with the Johnson's vapor bath
Good luck!