New Cat..Need for concern??

Ok, so i adopted a new kitty four days ago.  The clinic told me she is 3 years old, so I wasn't really anticipating any problems.  The first few days seemed fine, just her trying to get used to the new place.  I have a loft apartment, and she prefers to stay upstairs.  At first she hid under my bed constantly, but lately she has ventured out more, and even slept on my bed last night!  Her food and her litter box are downstairs.  She does use the litter box, but has barely touched any food or water since she moved in.  This is where I get concerned, because she seems to be urinating quite a bit, for the amount she has drank anyways. However I have caught her a few times drinking out of the toilet, so I can't be certain how much she has actually drank.  Today, when I went to clean out the box, I noticed a little red in the urine, definitely red though.  I left for a few hours, and the first thing i checked when i got home was the litter box, and again their was red in the urine.  She seems fine otherwise though.  She loves affection, and purrs a lot when I pet her.  I did notice her ears were cold, and a tiny bit of drainage coming from her eyes.  She doesn't seem to be in any pain, and she only meows when I come up stairs to check on her, and then she comes running towards me.  Do I have any reason for concern?  Or is it just her adjusting to the new place?  The clinic didn't mention and medical history.  And it is Sunday, otherwise I think I would be at the vet already!  I appreciate any help, and sorry this is so long!! 

Here is a picture of what I found in the litter box this morning too....Thanks Again!

Blood in the urine in young cats is usually caused by an infection, probably a urinary tract infection. It could also be kidney or bladder stones, but those usually cause pain even in normally-stoic kitties.

Is she spayed?

She should definitely see a vet as soon as you can take her, though I don't think you have to rush her to an emergency vet. If she's not showing symptoms like straining to urinate or pain, it's fine to take her tomorrow.

Welcome to the forums, and good luck :}

Yes she has been spayed.  Although she doesn't seem to be in pain, I have tried playing with her but she seems uninterested, and her not eating either worries me.  I have science diet, and she nibbled at it once her first night, but I think that's about it.  I tried to feed her wet food today, and she seemed to want to eat it, took a few nibbles then just went back upstairs and layed down. 

Could the trauma of leaving the shelter and being re-homed have caused this?  I just find it strange that the shelter didn't mention any problems. 
 

I imagine a cat can definitely be stressed by changes in environment. If she was at the shelter for any length of time, she may have gotten used to her surroundings and schedule, even if it wasn't the happiest time in her life. Conversely, if she was only at the shelter a very short time, she's changed scenery at least three times in rapid succession! Either situation can lead to stress, as cats are pretty sensitive to their environments. She should settle down eventually.

I don't think the blood in the urine would come from stress alone :/ It's hard to say for sure, but unless she has physically hurt herself and bruised her bladder/kidneys during running/hiding/etc. in her new home, she shouldn't be urinating blood just from stress.

Cats are prone to urinary tract infections and a whole host of kidney/urinary issues, most of which seem to stem from being fed a kibble diet and basically being in a constant state of dehydration. Though, if your new kitty is still peeing, she's probably not dehydrated.

A simple urinary tract infection seems most likely.

It's disappointing that the shelter didn't mention anything, though it's possible that they didn't notice blood in her urine if they're overworked or have a lot of cats that they're caring for.