Serial Number wont qualify MacBook Pro Retina, 15-inch, Mid 2015 Battery recall

That's something you better call Apple Support directly for help Contact Apple for support and service - Apple Support. They might ask you to go to an Apple Store or Authorized (an Apple Store would be better) to get your Mac properly checked. It might be that even if it doesn't show as eligible to the Service Program, they might realize that it in fact has the same problem and decide to include you in the program. Do not give up on the first attempt if you get a no.

About using your Mac in this condition, I strongly advise you not to. Good energy control (I mean good batteries, energy circuit boards, power supplies) is essential for complex electronic devices. Minor changes in it might permanently damage components, making your Mac behave erratic or simply kill it.

Go for service as soon as you can to avoid losing your Mac.

FYI, the Battery Recall only deals with a fire safety issue and not a swollen battery issue. These two issues are completely different. If the laptop is less than three years old Apple may replace a swollen battery for free under a secret free repair program (our organization has had Apple replace swollen batteries on our laptops that are less than three years old), otherwise users are required to pay for the replacement of a swollen battery.

You should do this as soon as possible as a swelling battery will damage other parts and, ultimately, may catch on fire.