@SarahGen-- I personally think that anyone who has been officially trained in this type of massage is qualified to do it.
I understand your worry about the cost and I think you should go ahead and have the massage done by a massage student. But make sure that he or she has actually been trained in lymphatic drainage.
You will most likely feel tired after the massage, this is normal. It means that you had some blockage in your lymphatic system and the massage opened it and allowed the toxins to be removed. Just rest and stay hydrated.