Speakers are getting distortion

I have a Panasonic df903u model, a pair of 6.5 type r components and a pair of kicker k525 5.25's.  The head unit pumps out about 22 watts rms to each speaker.  However, whenever I try listening to my music "loud" it begins distorting.  I'm not really listening to my music too loud, in fear of blowing my new speakers.  But I was wondering, did I wire anythign wrong?  Or is 22 watts just not enough to listen to louder music. 

If an amp is the answer at hand, are JBL's good with higher frequencies, I was looking at the 80.4 (i think, well the amp put out 50x4 into 4 ohms)  I've basically been looking at sub amps so I really have no clue what amps are good for 6.5's and 5.25's.

double check all your speaker connections are in phase...

also, low frequencies, even at moderate volume can cause distortion without sufficient power,,

if connections are good, you may need an amplifier, and JBL is fine

Oh one more quick question:  When wiring an amp to component speakers, do you just wiring directly to the crossovers, and keep the regular wires that run from the crossover to the driver and tweeter.  Or must you replace the wires that run from the crossover to the driver and tweeters.

I’m not exactly sure I understand your question. But the amps channel hooks up to the speaker input on the X-over. then there is a connection on the X over that goes to the driver and another that will go to the tweeter they should be labeled.