I think you're aiming at this: I got stuck in a long [line / queue]. I have no idea what you intend to convey by using "processions", which are basically slowly moving religious parades. You can't possibly "get stuck" in a procession.
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harry1999have stuckI have got stuck in traffic is roughly the same as I'm stuck in traffic. I have got stuck in traffic says that the beginning of being stuck was earlier and you have continued to be stuck until now. I'm stuck in traffic just says that you are stuck now.