Will I have to have anesthetic for a filling?

Hi! So i have got a permanent milk tooth as my adult tooth never grew in my mouth and my Dentist said I have a tiny cavity in the tooth and I should have it filled because I have to look after that tooth for the rest of my life since I wont be getting an adult tooth replacing it, otherwise she said she wouldn't have worried about filling it.

I assume it is quite a small cavity as she was willing to not fill it if I had an adult tooth to replace it and when I asked if I would have to have an injection or anything she said no unless it starts to hurt (which is great, i hate injections in my arm let alone mouth).

My question is, is the filling likely to cause me pain? I have had any fillings before without injections in milk teeth when I was young and don't remember any pain at all but looking it up on yahoo etc people are saying it's actually pretty painful?!

Thank you!