I'd Love Some Advice [Including Selfie]

Okay so a very old friend of mine (as in we've been friends for a while, she's not particularly old) just invited me to a party. This party is her big sister's friend's party, so I'll be surrounded by people I don't know too well (I've met some of them a few times years and years ago) who are all older than me (in their twenties) - the exception being my friend and her big sister, who I used to go to gigs with years ago. I know my friend wants me there because she invited me, and her sister because when she asked her sister which friend she should invite, her sister responded with "Lucy, she's not an ass."

There are two rules to the party.
1) You have to bring your own cup, but it can't be a cup (a bowl or a jar or something fun?)
2) At some point in the night you'll be tied to somebody else and you won't be untied until you complete a task.

The second part really worried me until my friend assured me "Don't worry, they're not horrible, they wouldn't tie you to somebody you don't know, you'd either be with me or my sister."

Thing is, as I've mentioned frequently on here, my social anxiety would wreak havoc on me. A party full of people I consider cool, all older than me and who I barely know. I want to go, but I know I'd be super shy and my self esteem would be less than good and I just...Gah, I don't know! What would you guys suggest?

Selfie with said friend (I'm the really really really pale one):


Selfie taken before the last party I went to: