Hmmm, bear with the questions please 
You've had the cham for at least the 3 1/2 weeks since he/she began shedding? Sorry if I missed it, but what species/locale cham do you have? Is the cham CBB or WC? Has he/she been eating, drinking regularly...and have you actually SEEN him/her eating and drinking? What are the ambient, cool side and basking temps of his/her cage? What is your hydration/misting schedule or set-up? What is the relative humidity of his/her cage? Have you contacted the breeder/seller to inquire about previous history and husbandry?
For immediate aid, I would recommend a long (20-30 minute) warm shower to aid in ridding the old skin and to hydrate him/her. If the cham does not freak out when handling, you might be able to use a gentle cocoa butter ointment to aid in removing the dead skin.
If the cham does freak out when trying to handle, then forget it! LOL 
As for his spikes "falling off", without photos of him/her no one can tell you exactly why, but no...they will not grow back and it is not normal for them to just fall off. Again, no one here knows the history of the animal or your current set-up..
I sincerely hope no one was trying to sell off, to a newbie, a sick adult cham they didn't raise correctly just to make a quick buck (or bunch-o-bucks!) before it expired.
Please provide more info about your cham, whatever history you have and your current set-up, so you can get help.
~ Laura