Is it safe to use betamethasone 0.05% ointment on my 3 month old baby's body for eczema? is it safe on the face? any side effects?

No…betamethasone is: High potency steroid & could damage baby's skin as well as interfere with growth if used too much. Hydrocortisone is lower potency; use 0.5 or 1.0% (otc) & the smallest amount that puts a thin film on affected area. Face is very sensitive area; so "less is more" applies. If 0.5% insufficient (after 5-7 days' use) may try 1%. Still no response, consult pediatrician.