To properly test for Giardia ... the microscope and slides should be sit-up ahead of time ... the moment the chinchilla's poop drops, it needs to be put on a wet slide and placed under the microscope. To be able to see the Giardia protozoa, it must be tested within 2 minutes of dropping (before it becomes cold).
Giardia is highly contagious. The cage and everything in it needs to be kept extremely clean until you are sure there is no more problem. Giardia is passed from a sick chin to a healthy chin when the healthy chin steps on a sick chin's poop or by eating it ... OR by a person passing it from one chinchilla to another, by handling the sick chin and not sanitizing their hands and clothing before handling a chinchilla that is not sick.
You might want to go to:
http://www.geocities.com/jobernstein1949/ and read the two articles on Giardia and Don't Let the Cure Kill Your Chinchilla.
Giardia will often cause dehydration, causing constipation also. If your chin has Giardia and took an anti diarrhea medication ... it got a double dose of constipation.
I always give acidophilus or live culture yogurt to any of my chins on any kind of medication. These should be given half-way between (at least 3 hours apart) doses of other medications.
Normally, I say NO NUTS ... BUT ... when constipation occurs ... an almond often works to help the chin get going again. Why take the change of giving it a nut? Because when a chins digestive system shuts down, death is usually not far away.
Keep a close eye on this chin, once prolapsed has occurred, it can easily re-occur. The stitch it to help prevent this. The brownish discharge could be diarrhea or could be a small amount of blood. Keep a close eye and keep the vet up-to-date on that and anything else that is not "normal" for this chin.
Jo Ann