Drawing blood for a test is not enough blood loss to exhibit faint and dizziness. It's usually a vaso response. Usually, when a person does that during a blood draw they recover as soon as the needle is removed. It could possibly be sore where they stuck you depending on what size needle and if they dug or just stuck you... I would think you are perfectly fine to work out. You haven't lost enough blood to be concerned. Now if you donate a unit of blood that is a different story..(I'm a Med Tech.)