OP I can actually help you here. If the blood is bright red, it indicates it is late in your GI track. What would of been more serious if it was black or darker color meaning it came from somewhere else earlier in your GI system.
Personally I had a very similar problem to yours not to long ago. A week ago I started bleeding after having a bowel movements out of the blue. The bleeding occurred only when taking a shit, but after 5 it still wasn't gone so I went to the doctor. He checked to make sure their weren't any masses in the area and then diagnosed it as internal hemorrhoids. After that appointment the bleeding stopped and hasn't come back since. You most likely have internal hemorrhoids as well. Since you say it felt like you were pissing it out your ass I am assuming you had diarrhea. This would make since constipation or diarrhea can cause internal hemorrhoids to occur. Regardless you should make an appointment to see your doctor. They will prob do a rectal exam, and possibly suggest some test if they feel it is needed.
As for it being weird for seeing your doctor about this... Well the doctor I saw was really close family friend of ours, and I actually just played tennis with him today. So I don't really think it gets much more weird than having a close friend preform a rectal exam on you. But then again I want to be a doctor one day so my situation didn't feel weird at all, it was just medicine.