Is it possible to make a solution of zinc oxide in a high school chemistry lab?
Zinc oxide is not soluble. It does dissolve at very acidic or alkaline pH, but it is a chemical reaction, not true dissolution.
The role of zinc oxide ( or titanium dioxide ) is mainly to cause UV light dispersion, effectively prolonging a lot the ray paths to allow sufficient absorption.  Dissolving the sunscreen formula would create a thin suspension with very different UV properties, which would have tendency for sedimentation.
I see a sense rather in measurement of passing UV through a thin film of a cream with zinc oxide, prepared by some controlled way, e.g. controlling its mass per area.

You have to do some sunscreen solubility tests first.
The used formula would be an emulsion either &quot;oil in water&quot;, either &quot;water in oil&quot;. The solvent should dissolve well both.  I would perhaps dissolve sunscreen in acetone, performing filtration/centrifugation or sedimentation, whatever applicable, to get rid of eventual $\ce{ZnO}$ or $\ce{TiO2}$ particles.
Then I would evaporate the aceton and add defined $\ce{ZnO}$ amount.
Or, you can try your own sunscreen formula.