The excess only comes into play if you claim from your own insurance for damages or losses. Not knowing the specifics of your policy, (whether you are a learner, NCB %, years of driving, annual premium etc) it is difficult to be specific in replies. As suggested by Sue Ellen, you may be best off ringing Allianz to discuss further.
You say that €1550 worth of damages were caused to the other vehicle - depending on the age of the vehicle, this could make it a write off or the person may seek depreciation for their car (if its a young model). There is also car hire to factor in whilst their vehicle is repaired for instance.
Either way, whether you decide to settle privately or not, you are obliged to inform your insurer that you have been in an accident.