The dose of U-238 isn't the problem. The large moving charged particle resulting from a decay of U-238 is. If you have paint on your walls then chances are you are breathing in a little bit of alpha radiation. If you are below ground level then chances are you are breathing in a little alpha radiation. Are you subjected to U right now? That all depends on where in the world (your location says Norway) you are. Certain parts of the world have higher concentrations of U than others (just like any other mined resource) so the levels of exposure depend on the concentrations of U at your location. Can I find U anywhere in the world--yes, but the levels of natural U in here in Michigan would require a lot more sample concentration that if I were in Nevada, or Niger.
Personally, I'd be more concerned with the radiation from the screen of your computer than from the alpha decay of natural U. I'd be more concerned with pesticide use than natural U or DU for that matter. I'd be more concerned about K-40 because most people eat Banana's or use potassium salt (BTW Morton season salt really makes a gamma detector click a lot-- if I recall we saw about 10 or 20 cps above baseline from common season salt).