So, although walkthroughs are not normally considered cheating, you should be sure that you've checked everything before using them. These are the things you should do:

First of all I suggest you go through the area you've played so far and:

• Check if you've missed an item somewhere
• Search the dead enemies' bodies, because they may have dropped an item
• Look for paths underwater
• Press Action twice while facing a receptacle or something like that to see if you can put an item in it
• Search for movable blocks or other movable objects by pressing Action while facing them. If Lara prepares to push or pull them, then they are movable
• Check if there is a trapdoor on the floor which opens as you step on it or collapses(and doesn't have spikes below)
• Look for openings above you. They are very common and in front of your eyes, really, so use your LOOK button
• Check if a wall(or other surface) is climbable
• Shoot all the widows and things like that with your weapons-they may be breakable
• Check if you can monkey swing from a ceiling e.t.c
• Look for crawlspaces
• Search for hidden passages
• Light up a flare and explore every room from corner to corner
• See if you can jump and grab somewhere. If you miss, don't give up, because some jumps are tricky. If the distance between the platform you want to grab and you is over that 5 squares you can't grab it form there. But if it is less that 4 squares you'll be able to grab it with a running and grabbing jump. Also, remember that pressing Action lowers the jump, so if you stand somewhere high and want to go far and land on a lower platform, you should do a running jump without pressing Action
• Try to find out what each lever/button/switch does and check if it is timed
• Examinate the buttons and the switches. By pressing some of them, something closes and something opens. So if you find an other way to get into the area that opens, you should press the switch again so that the closed thing opens and the open thing closes. You can access the area that has just closed though and something in there might have opened. In fact, that's the solution to many hard puzzles
• Find out why some things exist. Nearly everything in Tomb Raider has a reason to exist, so you should explore each objects that gets your attention closely. The designers help you, by making Lara look at some things sometimes. For example in Temple of Karnak, Lara looks at the ceiling as you enter it and it in Aldwych the floor collapses to make you notice the curtain where the ornate star is hidden
• Examinate the movable objects. By placing them in a special square on the floor something might happen
• Check if you can backflip form a slope or ladder and land somewhere else
• See if you can aim at something with the Laser Sight or with the Grappling Gun