Just do it!!! You will feel SO much better knowing you are okay and that it is nothing major other than hems. You need to think about how unhealthy it is for you to be feeling this way. I've gotten so many tests done that doctors have thought I needed for my brain and heart and uterus and everything has turned out completely normal other than having a abnormal shaped uterus. You are going to be FINE and you will feel so much relief. I don't think it's a tumor, and I'm 20. Doctor told me it's EXTREMELY rare for anyone in their 20s to develop any sort of cancer of the colon/rectum when I went in for constipation and a little red blood on the toilet paper. I say get the test done, and consider therapy after when you know you are okay so that none of these thoughts happen again. You are healthy and have a LONG life ahead of you. Enjoy it, get the test done, and once you know you're fine try to get these silly thoughts out of your head.
Also, my stool has looked like the picture you posted. It looked absolutely normal. :)