If we need to search Social media and extract vital information, perhaps the secret is in making best use of the search tools. I don’t use social media, so this is just from a quick glance on the web.
Twitter has an advanced search tool which you access at https://twitter.com/search-advanced. Thinking up clever search terms to put into here might be a useful skill.
There are tools available to allow you to download the results of twitter searches into the likes of Excel. Unfortunately, all the ones I could find cost money or provide far too many complex services which I don’t think you will need. Perhaps you will be provided with access to such a thing.
If you have got computers then use them as computers. Don’t rely on writing everything down on the table! See if you can produce see files on each others computers (there is normally a public folder on Windows which you can share with other users). Perhaps someone could keep notes of progress there are the others could load them as needed. If this is not obvious however, then don’t waste time trying to set it up.
If you are gathering lots of data then perhaps you need someone on charge of keeping it all in a sensible order (a librarian if you will) so that you don’t all waste time going “Where did we write down that use name we found”.
It is not clear to me whether you are just going to get normal user access to the social media information or whether you will have some sort of privileged administrator access allowing you to see more information such as details of IP addresses.
I will add more if thoughts come to me.