I live in a small town in Argentina and there is no special rice available for cooking with milk, like I am used to buy in Germany.
Which sort of rice is best for cooking with milk. It should get really soft while cooking.
You don't say what type of rice pudding you want to make, and wikipedia lists quite a few. I'm assuming you want to make a traditional british baked rice pudding in this answer, but if not then it might be useful to clarify what you want to make, as many cultures make different rice puddings and use different rices to make them.
I think you can make rice pudding with any short grained white rice. Traditional 'pudding rice' is just a cheap short grain rice, but you could use arborio, the traditional short grain risotto rice or sushi rice and get a similar result. This article outlines attempts at using a few different rices, with varying degrees of success.
The key to getting it soft when cooking is probably just a function of having enough liquid. Too little liquid and it'll stay firm, more than enough and it'll go soft & squidgy. Starchy rice (which white short grain typically is) will give you the sticky, gloopy rice pudding consistency.
This question might also be useful