Yes, you do need to go to the hospital of your water broke. They need to see if you're progressing. You can develop an Infection so if you don't deliver within 24 hours they like to start you in antibiotics. Then they'll monitor you, not necessarily in the hospital.
You do need to go to the hospital. They may or may not deliver you. They waited 8 days from when my water broke to deliver my son. My water broke at 32 weeks and 6 days. My son did great at 34 weeks. He had no lung issues at all. I hope all is well with your little one too!!!
They say you need to deliver within 24 hours of your water breaking or your baby can get an infection! 25 weeks is early and your baby will be premature but not so early your at really high risk, my mother in law had my brother in law at 28 weeks!
I don't know if baby's lungs are ok, but if your water broke you need to go to hospital.