She isnt drowning yet, her eyes are just watery so she can't see anything and the water started to get in and her lungs started to fill.
They surface and Pearl starts swimming to shore with Delilah, struggling against the waves that hit her and spray her with seafoam, trying her best to see through the storm, fighting everything just to keep Delilah alive. Finally, after hours of what feels like torture, she reaches the shore and climbs onto it, laying Delilah down