Which is correct?
We all started panicking and looking around to see if there are any unattended tickets around us.....
We all started panicking and looking around to see if there were any >unattended tickets around us.....
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If you're talking about actions or events that took place in the past, then use past-tense verbs to describe them. In your sentence, it is clear that you're talking about a situation that happened in the past (started is what indicates that), so keep the other verb in the past tense as well:
We all started panicking and looking around to see if there were any unattended tickets around us.
Whether or not the tickets are there now is irrelevant to the story. We care about whether they were there at the time of the looking.
You might be thinking that, by mentioning an event, you define a time-frame relative to that event; that the tickets' existence is considered to be in the present of the looking. I imagine that in some languages it does work that way (I would be very surprised to learn that there are no such languages), but English is not among them.
In passing, I'll note that “if there have been any tickets” would also be un-English, even if the main verb is in have done form. But you can say “I went to see whether the show had ended (before I looked).”