You have absolutely no chance to get anything close to it on your own, so just don't.
I'm afraid this is pretty much true, although the hobbyist in me doesn't like to admit it.
The amount of radioactivity you're looking for is small compared to natural background, and small even compared to the normal variations in background. To identify any un-natural contamination you'll need a detector capable of distinguishing different isotopes, in a low-background environment, and it'll need to be regularly calibrated with standard sources. That entails a lot more gear than a Geiger-Muller tube, all of which is very very expensive, not to say tricky to operate.
With a GM counter about the best you can do is to try to measure the radioactive decay of a sample, although most relevant isotopes have very long lifetimes which will be too hard to measure. 131-iodine is easy to detect and has a measurable half-life at 8 days, but I expect the authorities would find it before you do, and anyway most of it has gone by now.
Alternatively you might befriend a physicist at your nearest nuclear research institute. Even then he or she will need to be quite a good friend, because the time and effort involved is significant, and this kind of expensive gear tends to be permanently in-use.