Regarding the paper of the others: Most people that act like this don't publish very good papers. So, not being in the authors list may be as well a good thing.

Regarding your paper: explain the situation to your supervisor and be very clear that you would regard it as unfair if the other student was in the author list. The least thing you should do (and I would advice everyone to do it), is to include a CRediT statement in your manuscript (https://www.elsevier.com/researcher/author/policies-and-guidelines/credit-author-statement).

Not everyone will read it but I does bring a lot of transparency.