Is my sun hat protecting me enough?

[tina_perricone]

I have very fair skin so I know it's important to limit my UV exposure. The problem is that my skin is very sensitive, and I've had an adverse reaction to every sunscreen/sunblock I've tried (including pure zinc-based ones). So I limit my sun exposure, and wear a big wide brim sun hat and long sleeves and pants when I'm out in the sun.

I have a portable UV checker which detects the intensity of UVA/UVB rays.

So that helps me know whether I'm getting much or any UV light.

Often if I'm out in the sun, I'll use the checker pointed straight at the sun, and let's say it comes up with a UV index of 6. Then I'll try it again, still pointed at the sun, but from underneath my hat, and it shows up as a 0 or 1.

Here's what I'm not sure about. I can tell just by looking that the hat doesn't block 100% of the sun, and some parts of the weave of the fabric are thicker than others. Can I trust the reading on the UV checker in that situation? If I try it a bunch of times and I never get anything above a zero UV index, does that mean I'm sufficiently protected?

I know some amount of ambient light will always get in, bouncing off the world around me, and so on; if the UV checker reads zero under the hat, does that mean I'm fine in terms of the ambient light as well?

Thanks.