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I’m looking at the ticket
taking me away
But every time I look
it says another day

I am English teacher (among other things) and I would say that you are OK with this use of the -ing ending.

The word "taking," strictly speaking, should not be in the present continuous tense, since it is not literally true. BUT, we are talking poetry here. This little adjustment is necessary to maintain meter. That is enough to make it OK. But what is more, you have established present continuous tense in the first line, so using that tense in the second line is consistent. To NOT use it might be inconsistent to a degree that renders you expression less immediate.

You are stating the situation in the NOW. To do it any other way could lessen your connection with the listener.

I like this meter better, but that's just me:

I’m looking at the ticket that is
taking me away
But every time I look at it
it says 'Some Other Day.'

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