Series 1 battery swollen and popped off

Based on your situation, I recommend service.

Service Checklist:

• Apple Watch service pricing.
• Check AppleCare Coverage.
• Get your Apple Watch ready for service.

Click ▶︎ Apple Watch Service. ⚛️

Need more help?

• Call Apple Support at 1-800-APLCARE. 📞
• International Support. 🌐
• Contact Apple Support. 📝
• Chat using Messages. 💬

Click ▶︎ Check Repair Status.

An Apple Watch series 1 is rather old. I don't know if you still have warranty, not likely giving the age of the series 1 Watch