Hello moitri.dingal
The keyword in the management of constipation is patience. Many a times stool time becomes a war field.
Let us discuss under the following heading

How severe is the constipation: a 5 step approach for home
Why it is so
What are the diet manipulations required
When do we go for test
As a person working with south indian children for the past 27 years, I have no faith in drugs, with due respect to all concerned
Only indication for drugs is : when the child is struggling to evacuate the incarcerated motion. That too only a suppository, which your doctor will prescribe.
How severe is constipation
1. If the motion is dry with out traces of moisture
2. If there is blood in the stool
3. While passing motion child has pain
4. If child's face changes while passing motion: he strains as if he is pregnant lady struggling to deliver the fetus.
5. Instead of sitting and straining he stands and strains
6. Instead of pushing the motion out he is taking back the motion
7. Crossing the legs like a pair of scissors
All these point to a severe problems, and it will take several weeks for it to subside
Diet:
To stop cows milk which means fresh cows milk, milk coming in sachets and formula milk( which are also developed from cows milk)
Junior horlicks in hot water may be tried if he is adamant on taking milk. Preferable alternatives are Ragi powder boiled in water . if you are not used to this cereal, use any cereal you are using : powder , boil in water and add salt and give.
Plenty of fluids : water, butter milk, coconut water, fresh citrus fruit juices
No dry food like chips, biscuits
Plantains, papaya, Greens, egg can be given daily.
Try to use half tsp of gingelly oil, if you are used to this oil in your cooking

Avoid Television. Exposure to television in the first 3 years of life can lead to autism. Television exposure will make the child lazy
Do not insist that he should pass only in the potty. He can pass any where
Last but not the least bowel control comes only after 18 months
Best wishes