I've been swimming around for an hour last night and an hour today and except for finding something (not sure what) in an alcove with 3 jellyfishes, I can't find anything else.

I don't own a strategy guide and I refuse to use an online walk through.

16+ years of playing Tomb Raider games and I have never never ever ever used a strategy guide and an online walk through until I have finished each game twice.

Well, at least Lara doesn't run out of air and she can swim forever!

Sounds like your at the beginning of the game. i don't know what those things are called, but they fit into a door and you have to turn them to match up symbols on the door. I think one of those things is just laying out in the open, you can find it just after you have dived in

I'm at the part with the giant octopus.

Lara went around and moved a few gears around and picked up treasures and medipack.

I am at a part where she is supposed to jump from a platform to the top of a pillar.

I saved the game right before the jump just in case I get her killed and sure enough, she dies.

So I load the saved game again and it doesn't take me back to that spot.

Instead it takes me to the entrance of the chamber with Lara looking down at the giant octopus.

There is also a part there where Lara uses the Grapple Hook to climb up the side of the wall but then I can get her off the grapple hook line without killing her.

There is a ledge behind her and I can't figure out how to get her to jump off the grapple hook the it.