3 metres is too close to plant trees, even smaller trees, too much of a risk.

What about bamboo? That makes a very good screen and heights vary from the small ones (a couple of feet) but more usually 13 feet (Phyllostachys nigra for instance) and up to 20 feet. There are thousands of varieties, and you don't say where you are in Australia, and I'm sure some bamboos grow better in different parts of your country, so a bit of research is necessary. A careful choice is required - some run and a root rhizome barrier should be inserted prior to planting, to prevent it spreading too far, but the roots aren't like those of a tree, in other words, large and woody. It's just you don't want bamboo popping up between the paving round your pool from where its run underground.

www.bamboowholesale.com.au seems to be a good site, lots of info on different varieties.

It takes time for things to happen. Are you willing to wait at least several years to get the results you want whatever the planting? If not, then consider installing a pool privacy screen, there are all sorts to choose from.