If it's one of the batteries you can remove yourself, then it will be obvious if it's swelling because it will be splitting apart. Also, you can try the trackpad with the battery removed to see if there is a difference in how it works.
This is not so easy to determine with batteries you are not supposed to remove yourself.
One thing you can check--hold down the option key and click on the battery icon. If it says anything other than "Normal" in the drop down menu like "Check Battery" or "Service Battery", it is definitely time for a new one.
Also, if you have access to an Apple Store, they can run a stress test on your battery at the Genius Bar and evaluate your trackpad at the same time for free.
Good luck!