Move to Europe! We have lists on everything!
Ice cream usually contains cream, so, not vegan. However, sorbets can be vegan, and there is an increasing market in soy ice-cream (worth checking out any health food stores).
I know I keep banging on about the vegan society, but they have a list of what basic products are animal derived. As a general rule, be suspicious of things with a creamy or cheesey texture, and overly processed foods like ready-meals (they tend to use all kinds of gunk as preservatives).
http://www.vegansociety.com/html/food/criteria.php
Since you're still living at home (I assume) and going to school, you may find it difficult to cut out all animal additives. Make changes in small steps, and don't feel you have to be too hard on yourself (or those around you!) to begin with. Since you're still developing, you might want to pay quite a bit of attention to nutrition, and making sure you get a sufficient calorific intake (I know people who were pretty much forced to live off pasta or beans on toast as a teen, and got long term health problems)