What I usually do is send a paper application with post it note telling them to email a a confirmation of receipt (email me saying they got it...) If there is no email in a few days, I usually make a phone call. It's much more direct... And they can hear the passion in your voice...
In your case, drop an email saying that you've been anxiously waiting for a reply because you'd love the opportunity to help/work with/shadow a professional to gain vital knowledge of the field and to prove to yourself that this really is for you.