Yea being and doing the co conscious integration process does feel strange the first time around. You can find my experience with this in my blog here.

It is a weird feeling But it sure makes the funtioning level ALOT better because now that you have experienced that memory piece (otherwise known as parts, alter, and so on) you have full access to those memories that you experienced and there won't be any more acting out that memory piece. It is now concidered a normal memory not an alter. You will now find there are things you can do without those memories being triggered.

So happy for you.