In all disputes, I think it is important to assess what you require as an end result - how you are going to achieve that end result, and whose co-operation do you need to achieve that end result.
If you apply that system here - you want your manager to get his finger out and sort your paperwork and get your overdue payments.
For this, you need your manager's co-operation, so it may not be wise to go over his head without giving him a chance to sort the issue first.
Make an appointment to see him, and have a polite conversation based around your need for the payments to be brought up to date, and ask him if there is any issue with getting this done.
Try and leave with an assurance that he is going to sort this issue, and a date when he epects your payments to be made up.
If the date passes - contact HR and ask them if there is a problem with your payments - but do not infer that your manager has been dilatory, or inefficient - nothing feeds back down the chain as fast as criticism.
If that fails, then you have reasonable recoruse to your Union for some action.
keep copies of all written communication between you and anyone else involved.
Make notes of any meetings and phone calls.
Good luck.