Most cases of constipation are brought on by not eating enough roughage (hay is good) or drinking enough water. Make sure your chinchilla has a constant supply of roughage ie: good quality hay (always in cage) and pellets. If really constipated try 1ml of Liquid paraffin from a syringe. measure carefully. dont overdose. Some chinchillas will need a second doze next day. If they dont like Liquid paraffin try the laxative often used for children called Syrup of figs again 1ml for the average sized chinchilla. Often all it will need is a few extra raisins. remember to give roughage after feeding raisins as they contain sugar.
We have a forum should you wish to join. there you can ask Aileen more about your chinchilla being constipated.see pic below of the difference between a chinchilla constipated and another sample of well fed chinchillas (mine :))

Note dropping should 'not' be squishy and stick to shelves etc. dropping should sweep off shelves with a soft brush. Scrubbing shelves with a scrubbing brush is harmful to the pinewood. It loosens the grain of the wood and this in turn allows bacteria to grow in the cracks. If this happens get new wooden shelves. A scraper is best if droppings are sticking to shelves, then a wipe over with chinchilla friendly antibacterial wipes or hibiscrub.
We, when doing the weekly clean out would never use anything but Virkon, it's a great all round antibacterial germ killer. Bought from our local pet shop.To find a supplier of Vircon online just type it into your browser.