Hiii Deepak :)
Hope you are doing well
Don't shift your school. There is very genuine reason behind this. You have already done your 10th and 11th from this school and if you want to avail quota then you should do your 12th from the school.
It is the generally mentioned to do 11th and 12th from the same school to avail state quota.
And since you have done your 10th also then it adds up to your application and makes it stronger.
Also if you have done 11th and 12th from the same school it works as the proof for you that you are the permanent residence of this state and generally during the counselling sessions there is no need to provide domicile. But for safer side please keep it with you they may ask for domicile.
So, its better to continue in Kota to avail state quota  and do your 12th with your full potential.

All the best.
Hope your delimma is resolved. :)

Hello!
I will suggest you to keep on continuing in kota since its preferred that you have done your eleventh in kota so you must be comfortable. You need to understand that 12 demands mental peace as well if you shift now you will take time to adjust and then a lot of time would be wasted. So to keep utilizing the time stay in kota and prepare well.
Best wishes from us.