After the announcement of NEET results, shall I separately apply to your college for admission in to MBBS ? If yes, when shall I apply?

Hello,
No, you do not have to separately apply for counselling.
Once the results are out you must apply for all India counselling under which all the government colleges under all India quota are there. Here, after applying you will have to fill your choices for college preferences.
There is also a separate application for deemed colleges in the all India counselling website itself if you want to apply to certain deemed colleges.
In these counselling you must make sure to enter the college of your preference higher in the list and the low preference colleges later.
You should also apply to state quota counselling of your domicile state by applying after the state merit lists are out. There are separate websites for each state. Eg: in Karnataka counselling is by KEA.
In a the counselling you will fill up the online form after which you will have a choice of colleges in which you should fill the college of your choice in order of you preference.
Other than this, you can also apply for private seats in other state counselling under open category. In this case you have to apply to the respective state counselling websites.
Hope this helps.
All the best