Changing school after 10th is quite a common scenario these days. You can definitely do the same, if you are willing to do so.
Normally students change school if they are getting a steam of their choice in some other school or if they are not satisfied with their present school. But remember that the teachers of the school are very important. The better the faculty the better the school is.
The school that one is changing should be the one that you can adjust in easily. With changing school one will have to adapt to the new environment that sometimes might be difficult for the person. It can lead to a lot of emotional disturbances also, making it difficult for the student to concentrate on his or her studies.
So whatever decision you take, it should be taken with caution.