Translating a shirt

Hi again everyone,

At a blood drive I got a shirt that stated " I gave blood" in a few different languages. I looked forward to finally learning enough Chinese to translate my shirt. However, playing around with my dictionary and low level skills, whereas I might have thought it would be我给血  Wǒ gěi xuè    ,

it says:

我是献血者   Wǒ shì xiàn xiě zhě

doesn't that mean
 "I am a blood donor" instead? 

Also, should there really be a measure word in there such as :

我是一个献血者   Wǒ shì yīgè xiàn xiě zhě

or is no measure word necessary?

Would saying " I gave blood " be an 
awkward way of saying it in Chinese 
and that's why they put
 "I am a blood donor" instead? 
(That is if I translated it correctly ).

I have attached an image of the shirt 
so you can see for yourself and let me
 know if I am even close in my 
translation.