I don't know why. Is there a way to fix this? Manamune? Stop using too much abilities?

Stop using abilities. I never have mana issues with Caitlyn. There are really only a couple of times you should be using her abilities.

Q - Only use when you have a guaranteed clear shot, like if Taric stuns your opponent and there aren't a bunch of minions in the way.

W - Keep 3 up in bushes or zoning the lane.

E - Only use to escape or gap-close to secure a kill.

R - Obviously only use when it's necessary.

If I were to guess I'd say you're trying to spam Q too much. This is a common mistake with inexperienced Cait players. Remember, your Auto-attack range is better than any other ADC early in the game. Use this to harass instead of your Q. Only use Q to lay down a solid chunk of damage when it's DEFINITELY going to hit. (as mentioned above)

Don't ever buy Manamune on Cait. Sivir, Ezreal, or Corki maybe. .But never on Cait.

For build:

boots + 3pots
BF Sword
Zeal
Vamp Scepter

Then build Infinity Edge, Phantom Dancer.. Follow with

Blood Thirster if you're doing really well and farming a lot.
Guardian Angel if you have died even once during Mid-game.
Last Whisper if 1-2 enemies have over 150 armor.

I use E so much to slow someone in teamfights..
I'll try not to spam Q so much.
Thank you!
I'd like to change my build so I'm testing different ones...

I love playing Cait, and I am guilty of spamming my Q, and I have run out of mana at the worst times,its something I'm working on, but having a support that uses clarity really helps me a lot if I'm having mana issues.

Ugh

This is my style of Cait, just letting you know.

Q: Try your best to hit the enemy with no minions in between, otherwise do not use it unless both enemies (support and AD) are lined up.

W: Try to keep up with 3 traps if possible. However, never put more than 2 traps in a single brush, you really don't need that many traps in a single brush

E: Use as needed, this skill should never get spam on.

R: Use it on enemy whenever if they lack sustain, otherwise save it to pick people off.

Item:
Longsword + 2 pots or boot + pots (If enemy have a high speed jungler/ enemy support is blitz)
Vamp
Boot
BF
BT or Zeal
If went zeal, go for IE if possible, if you need sustain, go back to BT
the rest should be clear.

With Cait's natural range you shouldn't really need to spam your Q during the laning phase to harass.

Her Q is most important in team fights, especially in areas like the river where there are not many minions to reduce the damage.

Her E is a utility and escape mechanism, generally to keep your distance from enemies, or close gaps for a kill, but mostly for the escape. The slow is really unimportant for the most part, generally if you're relying on the slow to save you, you're a little too out of position and are probably going to die.

The only skill that really should be "spammed" is your W and that's only to maintain good positioning on your traps. If all of your traps have been placed down recently and are in good spots based on you and your enemies, then you don't need to use it any more.

R is mostly obvious, but don't underestimate R's use to help a teammate chase down or secure a kill, don't always just use it as a finisher.

Unless you've recently been in a few teamfights, there aren't many reasons why you should be out of mana as cait, even at early levels.

You just answered yourself!!! This is basically for every ADC in LOL

if your guilty of spamming then you may also want to look at having your support play soraka as well. This way you can harrass with abilities more.