Absolutely, I would strongly consider a emergency vet visit.
Based on your description and the symptoms, one concern would be stomach bloat or stomach torsion, which is life threatening. Any time a pet exhibits any change in breathing, as well as, any type of shaking/tremors, that is an emergency. It's improtant to recognize that these other symptoms classify as this being more serious since many many dogs will vomit for all sorts of reasons, but they don't shake or exhibit labored breathing.
Yes, having ingested ocean water can cause illness. Dehydration may be occurring, but not as the cause of the problem. As a consequence.
To help settle the stomach you can give a tablet of maximum strength 20mg Pepcid A.C. antacid, but I am strongly advising the ER vet visit under the circumstances.
If the vet is considered about any stomach tension or bloat, x-rays are very likely to be suggested. Good Luck!