If you can stretch your budget to around 25000 INR you can get 3BHK options in Redfields, which is near Sowripalayam. These are full of facilities and well sized around 1500 to 1800 sq ft
Hey. Individual houses are plenty in Sowripalayam area these days as it is a developing residential area. You can find 3 BHKs for Rs 6000 to Rs 15000 per month. It will be good for a large family as yours but price variation depends on the furnishing.