My arms gets bigger/fatter as I observe I frequently carry my child who’s 10kg now. Any exercise to get it back to a slimmer shape?

For me, planking (elbow plank or the yoga plank) is the best way to tone, strengthen and slim down flabby arms. Planking also tones the abs so you're killing two birds with one stone. You should try the 30-day planking challenge -- it starts off lightly, 20 seconds a day and slowly builds up as you grow stronger and more comfortable with planking.