Three months old baby, shaking his head while sleeping, there are several possibilities. One, the baby has heat sweating, resulting in the head cloth wet caused by. Two, may be the baby has ear wax caused by itching, can help the baby to see. Third, due to the baby’s organism needs more calcium, fast growth and development, insufficient sunlight, and caused by calcium deficiency. You can take your baby to the hospital to have a laboratory test for trace elements to see the extent of the baby’s deficiency. If the baby is deficient in calcium, to timely supplement, you can give the baby supplement vitamin D3 or calcium carbonate granule punch, to strengthen outdoor activities, more sunshine, so that you can promote the absorption of calcium.