Hi, MR SMITH, I appreciate you are very alarmed and anxious. Perhaps you would phone the National cancer Helpline 1800200700 and you will get information and a listening ear to your predicament.
Even if you take out private insurance today, benefits will not kick in immediately as there is a waiting period depending when you gave up your cover.
You don't want to upset your wife's exams, so you could if you want go see your GP who will start the process of identifying your problem. When the exams are over tell your wife what has happened and why you kept it to yourself. If you are as stressed as you say, your wife will probably notice ?
So, try phoning above no. and I would presume they will advise best course of action Good luck.
As far as I have heard you will get through public health system fairly smartly if you have to go for tests etc.