This answer is part of Pet's Spring Cleaning Campaign. This question is old, but this answer will still help people with the same problem.
Rats (among other animals) have a Harderian gland at their eyes that excretes porphyrin - a chemical compound very close to hemoglobin, the compound responsible for the red color of our blood.
If the rat is stressed, ill, in pain or malnourished, this gland excretes more porphyrin, which can be visible as red tears, a brownish black crust around the eyes nostrils or the hands (since rats rub their hands over their faces while grooming).
This article Those red tears: porphyrin and the Norway rat lists possible causes for excess porphyrin production. In addition to acute pain and stress, these are:
A number of diseases are also associated with the overproduction of porphyrin, such as corynebacterium, mycoplasmosis, salmonellosis, and sialodacryoadenitis (SDA) (USF Div. Comp. Med. PDF ref). Dietary deficiencies may cause porphyrin overproduction as well (Sakai 1981).
These lists are not comprehensive, but rather go to show that porphyrin overproduction is a non-specific response to stress, pain, disease, or poor diet.