I was kicked and have doomsday point. If I go back to same alliance again, the point get back or not?

Yes, you get your points back.

If you are in alliance A, and earn for example 10,000 season points, and leave to go to alliance B, you have to earn new season points in alliance B. If you earn 5,000 while in alliance B, then leave B and go back to alliance A, the 10,000 points you had before in A will show up again but of course you will lose the 5,000 points earned while in alliance B.