You should be proud of yourself not feeling like shiat. Your worried about your DD and your seeking help through the right channels ie GP then specialist. Usually the specialist wants results as otherwise they will send them off anyway which is expensive if a specialist orders them as opposed to a GP plus more waiting for answers.

Its not nice to subject your child to blood tests but if there is a problem better to know sooner rather then later. Can you have a pathology place do it as opposed to a GP? They are usually alot more experienced and use a butterfly needle as opposed to something the GP may use.