I am so sorry that your mom responded as she did and caused you further anxiety. Sometimes when a girl begins her menses, especially the first few times, it can be more of a spotting, brownish discharge. It sounds like you are experiencing your first menstral cycle. Can you talk with a school nurse, health teacher, or peer or other trusted adult like a friends mother? Someone who would be willing to discuss the changes a girls body goes through when becoming a woman and different types of sanitary products available?
I think you got your first period and it is nothing to worry about. It is normal for it to start out slow and brownish to pink. Just use a pad or a tampon. As for your anatomy, I your pee comes our of you urethra which is a very small opening I doubt you got the toilet paper in there. Your vagina has many parts to and you should become familiar with them. Use a mirror and check it out. Look up pictures of the anatomy so you know what's where. If the blood is coming from your vagina which is the larger hole between you butt and clitorous then it is your period. Your first few periods might be irregular (kind of stop and go even passing clots). If the blood is mixed with your urine then you might have a bladder issue but I don't think this is your problem and you would likely have other symptoms. If you do have a fever, urethra pain while urinating, ugrency to go more than usual, pain after urinating, lower back pain ( sometimes hard to tell from cramps) then you should see a doctor as it could be a bladder infection which is easily treated with antibiotics but you want to take care of it. I am surprised your mom is not more helpful with this. You can always ask your school nurse.