This is for piano btw.
For a typical G7, I would play: LH: FB RH: EAD or LH: BF RH: AEG
For the first version, would I alter the D to D#? For the second version, would I alter the E to D#?
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On the first form (FB on LH), for a G7alt (G7#9b13) I would definitely play FB-EbGBb.
So for a G7#5 (aka G7b13 or G9b13 since the 9th is just an added color) I would start from the previous and play FB-EbGA. This gives you the freedom to move the A to Ab (becomes a G7b9b13) or to the A# (and you are back to G7alt).
For the second form I would do the same as you play, so BF-AEbG