I know that this question has been asked a few times but my situation is a little unique as you will see.
Approximately two weeks ago on a Monday I received a verbal offer for a summer internship program. The person who called me and made the offer was the one who interviewed me, and they said that I should receive an employment contract emailed in that week. They also said to contact them if I had not received an employment contract by the Friday. Friday came around with no email so I sent the person who gave me an offer an email to let them know. They responded the following week and said that they would get onto HR and let me know once they've heard back - they also confirmed I received the email by calling me. It has now been 8 days since the last contact and I have not heard anything from HR or from the person who made me the verbal offer.
Because of this, I don't know the start date (all I know is it's sometime in November) or any other information about the job (apart from location).
Given this is for an internship, it's my first time in a professional role, so I'm a little hesitant to call and ask for updates lest I come across as needy or annoying. (but keep in mind I'm pretty excited to have received a verbal offer for an internship - they are quite competitive)
What should I do?