If your baby is 2 months old and has a cold, the best home remedy is breast milk. In fact, infants who are up to 6 months do not need any medication other than breast milk when they get cold to prevent the bacteria and virus.
Breast milk has antibodies that can help to build immunity in the baby's body to fight with bacteria, viruses and germs. In addition, it keeps your baby hydrated.
For know more about antibodies properties, you can go to https://medlineplus.gov/ency/article/002223.htm