Is automobile engineering comes under mechanical engineering or is it a separate trade??

Both are different. Mechanical engineering is having not only machines, there are so many included in that like fluid dynamics, kinematics, Dom, material science and also just 6 months for automobile engineering.
But in automobile engineering, they'll concentrate on different types of automobiles, how they made, materials used, mechanism etc.., it's only of machines.
All the best. Choose decision wisely.