I have a simple question:
No, you can't
It says clearly in nondetection's spell description:
The target can't be targeted by any divination magic
"Any" includes your own, so no divination spells would affect the target, unless that spell says otherwise.
Detect magic is an AOE spell that targets the caster as the point of origin as stated in the rules for targeting:
A spell's description tells you whether the spell targets creatures, objects, or a point of origin for an area of effect
And thus the spell cannot target the caster.