how Botox can cause a systemic effect such as feeling ill, is not well studied. Certainly quick uptake by the venous circulation might cause symptoms when normal injections in the dermis or subcutaneous tissues or muscles would allow for a slower uptake of the medicine and less peripheral symptoms. If there is a drop of blood or a bruise, it doesn't mean the Botox went in a vein though. The needle stick can disrupt the vein wall before or after the Botox is introduced to the surrounding tissue. Vague symptoms are rarely reported and when they are they tend to be self-limiting.
The information provided in Dr. Shelton's answer is for educational purposes only and is not intended to constitute medical advice. The information provided should not be relied upon as a substitute for consultations with a qualified health professional who may be familiar with your individual medical needs. If you are experiencing a medical emergency proceed to your nearest emergency room.