We don't know your amplifier specs.
Here is what your missing:
Dead key is the carrier only.
100% modulation added to the carrier would be a 'peak drive' of 20 watts if the dead key were 5 watts or 5x4=20.
If this overdrives the amplifier on peaks there will be distortion and splatter.
You have to understand the principle of the operation.
The amplifier gain spec has to be known or an accurate honest input /output power specified or you don't know what you need to do for correct drive.
.
Here is an example:
On a 30 watt in/160 watt out, FM could be used at the full 30 watt drive.
But to use this same amp on AM the drive has to be dropped all the way down to 7.5 watts carrier because 7.4 x 4 = 30 watts max drive the amp will take at 100% modulation.
Where did the #4 multiplier factor come from?
It's normal AM modulation science that 100% modulation is equal to 4 times the carrier power.
If an amplifier is driven harder it goes into gain compression causing distortion, splatter and excessive harmonics.
Some possible problems adding to distortion are a mismatch between the radio and amplifier and mismatch at the antenna.
This very often shows up as RF getting back into the mike line because your whole setup becomes RF hot on the outside.
You need to sort out the drive level first then be sure the matches are all less than 2 to 1 SWR.
On CB, lack of this knowledge brings about a lot problems that are not understood.
Good luck.