Hi,
Intro Week at Sheffield is a huge event, and there's loads of stuff to do, particularly within the Union, including film screenings, culture evenings, orientation events ( so you can get to know the campus and the city) and trips out the Peak District. There are nights out at the Union if that's what you're into, and these are very good/ popular, but that's only a small aspect of Intro Week and the stuff you can get involved in.
Activities Fair and Sports Fair both run in Intro Week - at these, you can and browse all the different societies and sports teams on offer at Sheffield, meet those involved and see if anything takes your fancy. Our 'Give it a Go' team also run a great (and huge!) programme of events for new and returning students. Give it a Go allows students to try out activities and societies at a beginners level - the sessions are all one-off, but if you like the activity there's the option to go along to more sessions in the future (they also run trips to Alton Towers, Chatsworth House and other places). Don't be worried about going along to a session by yourself, as plenty of people do this - it's a great way to meet like-minded people in a friendly, informal environment. Alternatively, Give it a Go sessions are also a fun way for you to bond with your flatmates and try out something a bit different.
Your department will also run orientation events for new students, allowing you to meet people on your course, your lecturers and the people who run your academic society. If you're living in university accommodation, there will also be events going on around your residency for you to get involved with (which you can find out about on moving weekend).
I also had my birthday in Intro Week, and I felt exactly the same as you - a bit worried that I wouldn't be able to celebrate it properly! However, I needn't have worried at all - even though I had only known my flatmates a couple of days, they decorated the flat for me and baked me a cake, and then we all went for a meal and to the Union, and I had a brilliant birthday. I would suggest picking something you would like to do for your birthday (maybe something you wouldn't do at home, just to avoid those major homesick feelings), and then inviting your flatmates (or whoever you meet in Intro Week) along. Remember, everyone is just as scared and nervous about making friends when they come to university, so I am sure whoever you are living with would be very happy to celebrate your birthday with you.
Hope that helps you out a bit, if you've got any more questions then just let me know!
Best wishes,
Georgie, Student Communications Team at the University of Sheffield