Confusion in deriving formula for fourier tansform of impulse train
What makes you think it's wrong? You're just not done yet. In your final expression, if $\omega n T $ is a multiple of $2\pi$, you'll sum "infinitely many ones" which gives you "infinite", whereas for other values, you're going to some numbers "equally spaced" over the complex unit circle, which gives you zero. This is exactly how a train of deltas behaves.

Of course this argument is very handwavy and somewhat dangerous as these intuitions may mislead us when making statements about infinite sums.

As a suggestion: try with a pulse train of the form $\sum_{n=-N}^N \delta(t-nT)$. Compute its Fourier transform. Then consider the limit $N\rightarrow \infty$. You should get something like $\sum_{n=-N}^N {\rm e}^{-j\omega n T}$, which you can simplify using the geometric series. Then, forming the limit over $N$ should be easier.