Do baby bottles that contain BPA hurt baby if I never heat them up? I am trying to breast feed and also pump?

BPA is not supposed to effect the anything unless you heat up the bottle or poor hot liquid into the bottle.
So simply warm the milk to appropriate temp then poor into the bottle or simply give it at room temp.
You could call the number on the bottle box and ask if the bottles contain BPA.

When you say never heat them up I assume you mean with the milk in them. But what a lot of people don’t think about is the process of washing and/or sterilizing the bottles heats them up as well and this process over time has the same effect of releasing the BPA substance which MAY pose a harm to children over a prolonged period of time. If you look at the studies done on this you may be able to determine how often you can wash a bottle before it becomes a concern and then replace them after so many washes (could get expensive though)