Rats commonly get resiratory problems. The new cage mate could have carried in the illness, and the stress of the situation of introducing a new friend, and the young age of the rat all make it easier to get a respiratory infection. You might want to think about the cage set up too. The bedding/substrate you are using, pine and wood shavings can be dusty, and may cause the sneezing. The location fo the cage, if it's by a window or in an drafty area, that could cause the sneezing. Also, the product you use to clean the cage could be a factor. If it leaves a chemical residue that may cause sneezing. Make sure your cage is cleaned often, out of drafts, and in a warm location. Use a dust-free substrate, and clean with dish soap and water dilution. I would suggest getting her in for an exam at your veterinarian, but if that's not an option at this time, monitor her at home. If her sneezing becomes constant, and she starts to sound funny when she breaths you would definetly need to bring her to your vet. The red on her bedding could be blood if the new rat is nipping her, otherwise rats commonly can get chromodacryorrhea, which is red tears/nasal discharge. Its caused by a pigment that is realeased from a gland behind the eye. It is not actually blood coming out of the nose or eyes. The pigment being released causing this usually happens during times of stress or illness, so a trip to your veterinarian would be beneficial to your little baby, just to rule out any illness before it gets worse. Hope this helps, and good luck with your critters!