I suggest you to have a good

talk with this co-worker first.Calm it down right now and think about why he reacts like that. Because your tone or something else? It is true he is not your secretary and no obligation to do whatever you ask him to do. At this situation, you need have good personal relationshipt to ask someone for such favor. More Polite tone like: "would you pls do xx for me because... " will be very helpful.
If you just go ahead to report it to your manager, maybe your manager will fell like you are weak in handling co-workers'relationship.
Also you might look at yourself carefully to see if there are anything you might need to do to in order to have a better working relationship with your co-workers too.
Of course if he does not accept any kind of your efforts to try to improve the team work relationship, then you can go directly to your manager and explain all the efforts you have done and ask for help. Then your manager will be on your side.