Is this from my car battery?

I have a 2001 Ford Escape v6 engine. The battery light has been on for almost 1 year, but I was told it could go on for a while. Lately, my car feels like it just doesn't want to go. The check engine light is not on. Is it finally time to replace my battery or is this from something else?

Added (1). I actually had my battery checked out at 3 places and they said that the battery is too small for my car. The light has been blinking on and off for a while now.

Get it to a shop and have the charging system tested. Whoever told you to continue driving with the battery light on is someone who knows nothing about cars.

If the battery is good then it's your alternator.

Here is more wrong with your car than just a battery it needs a regular service by the FORD dealer and and a diagnostic test to find the fault by a ford dealer. Because it has a problem.

You may have a brake caliper hanging up. You exhaust may be restricted. If the battery is staying charged then the alternator must be charging enough. It could be charging to high though or have some ac content. Cars don't do well with those two things. Time to get the alternator actually checked.