Yes, you can use "nicht mehr" in that way. But people might think that you are trying to imply that you went to the cinema several times before and now you cannot go any more because of your test.
So if you just want to say "I was planning to, but now cannot go" without making any implications about the past, then a better way to phrase your sentence would be:
"Ich hatte einen Plan, ins Kino zu gehen, aber ich kann doch nicht gehen, weil ich eine Prüfung habe".
But like I said, your sentence is totally correct too and people do use "nicht mehr" for that.