the led can range from 5 to 9 to 12 to 14 volts .So I thought the led isn't getting a consistent voltage cause a car voltage goes up and down.Yes the voltage is 14 v at its highest but a car voltage goes up and down . Remember every time you turn on something in a car the voltage goes down the back up .
You obviously have never measured the voltage at your car battery. When parked, the voltage will be 12 to 12.6V. With the engine running, even at idle, the voltage will be 13.5 to 14.5V. A few minutes after a start, the alternator will bring the battery voltage to 14.25V +- 0.1V. This will vary a little with ambient temperature, the hotter it is, the higher the battery voltage.
If you designed your current limiting resistors for an input voltage of 14.4V, what do you suppose would happen if the engine was stopped, and the battery voltage sagged to 12V? Answer: nothing, except the LEDs would be a little dimmer, they would run cooler, as would the current limiting resistors, and they would be less likely to burn out...
The leds are in the headlight . They are mounted in a plastic cap that fits nice snug
There is your problem!!! The LEDs must be mounted on a copper heatsink. Download the data sheet or application notes from the LED maker's web site. They will specify how the LEDs are to be mounted. The LEDs produce heat (lots of it) when lit. Having them bottled up in a closed container is very bad! Not having them mounted on a large metal substrate with many square inches of area per LED is bad.
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The resisters are 8 inches from the led raped in heat shrink....
The resistors are dissipating even more power than the LEDs. If you start with 14.4V and the LEDs each have a forward voltage of 3.2V, then the resistor must drop 14.4-3.2 = 11.2V Since the current through each LED and each resistor is supposed to be 0.09A, the resistor should be 11.2/0.09 = 125Ω. The resistors are dissipating 11.2*0.09 = 1.008W, so they should really be 2W resistors. What are you using?
Wrapping a 2W resistor in heatshrink will reduce its ability to dissipate heat, and will likely start a fire...
Using one resistor per one LED is very wasteful. I would connect three LEDs in series with one current limiter (resistor or more complex current limiting circuit)