I can't know what it's like to swim with CP, but based on your description of fighting the water and becoming exhausted, you're experiencing the same things as many beginners who are fully abled. My sense is that most of the problems you report are related more to inefficiency than CP...which ought to be highly encouraging.
The most common causes for inefficiency - and their solutions - are described in Chapter 3 of the series of chapters from my next book, posted in the Outside the Box conference. If you've not read that chapter yet, why don't you do so now and let us know if any of those universal "problems" of new swimmers apply to you. If so, then you'll have some good news -- your sense of fighting the water and your exhaustion can be solved by learning new skills.
Head Coach & Chief Executive Optimist
May your laps be as happy as mine.
My TI Story