I would purge the vessel and your solvents with inert gas; and shield the vessel from light as much as possible. If you use dry DMSO, I would not expect difficulties.
There are a lot of things in DMEM; hard to say wether any of them could react with your compound. Maybe you can try to get nmr with water suppression at the start of the period, and compare the spectra with ones taken every few weeks to be sure.