Is it true that baby can catch cold and cough when teething? If yes, why so? Are there ways to make baby feel better rather than giving them synthetic medicine? TIA!

Hmm. First time hearing about them catching a cold & cough during teething period. Give baby something to gnaw on for those aching gums. If baby is down with a cold, i would recommend letting baby sleep slightly elevated so the mucus will not flow backwards and block his nasal passage which will tend cause blocked nose.