Hi chandni, 

You have chosen government colleges in the neet ug counselling of Uttarakhand then you will be alloted a seat according to your marks in that colleges only and you will not be able to get government quota seats in private colleges if you have not chosen them in choice filling. 

And if you want to have private colleges with government quota then you can take the seat alloted in first round and can go with upgradation option for second round there you have to choose private colleges  then if you don't get any private college then you can participate in the private colleges counselling of your state private colleges but they will be expensive. 

For any other information you can ask us.