Is it normal for some of my bydureon to ooze out after an injection?

I also have som oozing after injection into my abdomen. I had blood once after injection into thigh. It's a not a lot of the medicine but maybe 1/8 of it? Wonder if that is normal?

Are you injecting into your abdomen? You should pinch up some skin inject yourself, remove the needle and then let go of the skin. Bleeding is unusual which is why I asked about your technique for subcutaneous administration. A tiny spot of medication coming out after administration is not unusual.