You need to buy a medicated antiseptic shower gel from the pharmacy to wash the area during shower. Dont use soap for any reason or shower gels from the supermarket. First thing that comes in my mind is a fungal infection without excluding other possibilities like psoriasis or lichen sclerosis etc. But i wouldnt go that far for now. I would recommend an antifungal cream from the supermarket like clotrimazole ( i m sure they sell it over the counter ) every night after your bath/shower or every morning depending what time you get your shower. Wash thoroughly with the antiseptic shower gel, rinse well and after you dry the area with a separate towel apply the cream. In case it doesnt respond to these you need to see a dermatologist for further investigation. And last but not least you need to wash your anal area everytime you use the bathroom to pass stool. Forget toilet roll for some time. Good luck
As it is on the one side of the anus, is this patch flat or lumpy?
As your bowel movements are not very regular and it is likely that you may be straining, it may be a haemorrhoid.
The other thing that can cause a lot of itching in the anus at night time is having threadworms.
Make an appointment with your GP (your normal doctor).
You do need to have it investigated, the doctor will examine you and will be able to say what the problem is and treat it accordingly.
Although N-Johnny30 has given some good advice about not using soaps, bath and shower gels, I would not recommend you buying any antifungal creams. Your doctor will prescribe or tell you what to get after he has examined you.