I know that V43 is a better option but the exercise I am doing does not allow me the option of inverted 7 chords. Can someone please correct me if I have made a mistake?
I don't see any problems here! You obviously can't double the F♯, and doubling the bass A would lead to parallels, so your only option is to double the C.
But there is one caveat: some traditions are really strict about motion from a diminished fifth to a perfect fifth, and thus they may view the upper-voice motion (soprano and tenor) moving into the I6 to be an error. I don't remember what Aldwell and Schachter say, but you'll want to clarify that they "allow" this if you're trying to follow that book exactly.
For me, I see this motion far too often in the literature to treat it as a part-writing error. There are chords later on where you can't resolve the tritone "correctly," and for that reason I personally think outlawing d5–P5 motion is pretty unnecessary.