that you get from the venepuncture area after the sticky plaster is applied is usually a reaction from the rubber in the plaster. Occasionally, how the phelobotomist (person who does the drawing of the blood) inserts the needle into the skin can be cause why the site looks red raw or purplish later on. This is a reaction of the stainless steel needle and the force of the puncture. If you are fair skinned, the effect is more obvious.
Rubber reaction is usually not a serious thing, unless you have latex allergy
that is IgE (allergy antibody) mediated and requires consideration if you react to gloves, condoms, rubber slippers (itchy legs) etc. Avoid the cheap rubber plasters next time. Just keep the area pressed with cotton and don't fold your arm at the elbow, so the bruising doesn't occur.
I hope this answers your query.