Unfortunately, you may be out of luck. That phone hasn't been made in years, and that means the battery market is equally dead. Any "new" battery that's still for sale is most likely old stock that has already deteriorated to some extent. I wouldn't trust any of them to be as good as a fresh new OEM battery, but I would still replace it just to get that swollen battery out of the phone and properly disposed of (it could soon become a safety hazard).
Do not throw it in the regular trash or self serve drop off battery recycling boxes, as it could be punctured easily and cause a fire at any time. Make sure to take it to an authorized battery recycling center and let them know it's swollen before dropping it off so they can take the proper precautions. You should also carry it in a sturdy container to prevent accidental punctures.[/I)
You may get lucky and get a good battery next time. If not, it is still better than a swollen battery. In that case, I'd look into a battery case or a separate battery pack.
Battery case pro: It's a case with a battery inside it to keep your phone charged for a seamless look.
Con: These may have some old stock issues as well, you'll lose access to the USB port (at least while the case is plugged in), and you'll be limited on looks/protection offered by the case. These aren't very popular and may not be available for your phone.
Battery pack pro:
Commonly sold universal designs, so fresh stock shouldn't be an issue as long as you stick with well known brands. Can get these in multiple capacities based on your needs.
Con: You'll have to tether your phone to it to charge, which may pose some problems with on the go use (even if just an aesthetics issue).
Of course, given the age of the phone, it may simply be time to consider upgrading it. I wouldn't be surprised if you're having performance issues, plus Samsung no longer supports it with OS and security updates.