Can a 2 month old catch a fever from someone who has one and is in the same room as them? will breast milk help them not to get fever?

Fever is a symptom, : not a disease. Breast milk is protective by both specific & non-specific immune factors. However, unless you know the specific virus or germ that caused the person's fever & how it's spread--by droplets in the air, saliva, contact with poorly washed hands, etc. -- no one can tell you your baby's exact risk of having been exposed or his exact chance of developing the infection himself.

Preventing infection: Breast feeding is great in providing stronger immune system in general, but if the infant is exposed to persons with febrile illness, there in no guarantee he will be protected because the virus or bacteria can be airborne, so just being in the same room can get them sick, make sure you keep the immunization & well baby check up appointments with your pediatrician. Good luck. Enjoy your baby.