Can the doctor tell your bulimic from blood tests?

I'm going to get a blood test in 2 days to check my b12 levels as my body can't absorb it from food so I get injections every 2 months. I have started making myself throw up after everything I eat or drink apart from water, it's been happening for just 3 weeks, I was 121 pounds and I am now 106 will they be able to tell? I'm planning on eating and not purging that day if it helps?