Welcome to the forums there
@Ireneh ..
Unfortunately, we might not be able to help you to much with this. The Trailblazers that we work on here on this forum, they quit producing back in 2009.
I do know there is a reset procedure for a new battery install. Your truck, being only 2 years old, I would think is still under warranty. I would check with your local GM dealer.
I will add this, I would not tell them that you installed a new battery, just tell them the 2 errors.
The reason I say this, the dealer is looking for ANY reason to screw you, and if they can trace the fault back to something that you did, installing a battery, then they are going to try to find a way to charge you for it.