Though it's marked as "resolved", I'm going to add a couple thoughts.
Grammatically correct? Yes and no.
Let's take the second sentence first. Consider this re-write.
"She had been extremely frightened and decided to save her breath, submerge, and push herself off of the wet sand."
The commas pause the action in the sentence and separate ideas for the reader/listener. (Also, note the inclusion of the possessive pronoun, "her". I think that makes things more clear and consistent with the subsequent use of the word "herself".
Overall, the three sentences are understandable, taken together. But there's a mix of tenses used: realized, had been going to drown, had been frightened, decided, managed to survive. This creates uncertainty about what was going on until the end. Only after reading all three sentences is it clear that they all relate to one continuous event that has ended.
Just something to consider.. Hope this helps.