If you can get it to Advance Auto Parts, I believe they'll check your charging system out for free (to verify it's not a problem in the car's charging system that's preventing the battery from getting charged) and, if it truly does need a battery, they'll sell you one and install it for no extra charge.
If you look at the battery where the two cables connect and find those connections to be corroded (generally will have white powdery stuff on them), that alone can be the cause of charging/starting problems. Regardless, Advance Auto Parts (and probably other places as well) can check it all out for you.
Your Honda car does not require a Honda battery.
But if the car's still under warranty, you'll definitely need to contact the dealer to see how best to handle it.
Bill