Attending hospital for an x-ray is to my knowledge, part of a diagnostic assessment in order to find out what is wrong. If you want to by-pass your GP, then you will have to be examined by a doctor in A&E or outpatients before any x-ray will be carried out. Given the current waiting times and queues in public hospitals - this could take hours. It may be faster to actually visit your doctor - after all, how do you know that you actually have sustained this injury and it is not something else?
The charge for attendance at the out-patients, accident and emergency or casualty department of any public hospital in Ireland is 55 euro. These fees are set each year by the Dept. Health and Children. You will have to pay this if you just turn up there without being referred there by your GP. There is no charge if you are referred by a GP. The current charge of 55 euro also does not apply if you hold a medical card, are being treated for an infectious disease, etc. If the charge would cause you undue hardship, then your HSE area may waive these charges.
I see your options therefore as being:
(a) vist your GP and pay for your visit. If you're referred by GP to A&E or outpatients Dept. of a public hospital then you won't have to pay the daily hospital charge of 55 euro. Pro's of this option are that your GP can rule out other injuries in advance of your trip to hospital and you may obtain an appointed time to turn up for your x-ray. Another pro of this option, is you are entitled to time off work (without pay) to attend hospital appointments. A further pro, is if your GP charges you 45 euro for a visit, you will save 10 euro by visiting them first, instead of forking out 55 euro to the A&E.
(b) by-pass your GP and go straight to hospital. You will have to pay the 55 euro A&E/out-patients charge and will have to wait to be examined by a doctor before you can be referred for an x-ray. Pros of this option are you get to see the fantastic health system in Ireland in full swing.
Remember in relation to hospital charges, if you have to return for further visits in relation to the same illness or accident to A&E or outpatients, you do not have to pay the charge again.