The eczema of your four and half month child could be Atopic Dermatitis wherein there is an eczematous condition of the ares of the skin especially the folds of elbows, knees, dorsal region and finally affecting the face too. It causes severe itching and on scratching there would be some oozing, rawness and secondary infection of the area.
Any suppression of the spot with some ointments would be deleterious as it can cause respiratory ailments like bronchitis, bronchial asthma etc.
Homeopathic Medicine has good remedies like Thuja, Ars, Bacillinum, Medorrhinum, Merc sol etc. to reduce the itching, lesions and preventing the recurrence. The disease has its phases and may not disappear at one time. There could be episodes of recurrence but everytime they would be lesser in intensity and frequency before altogether disappearing.