post a good picture of it
is your leg extension set correctly?
Is your headset smooth, with no play in it?
do you understand that the primary position, is resting your hands on the brake hoods, not in the drops?
Are your brakes even setup well?
There are quite a few things to look at, like learning to ride, and servicing the bike, before you 'modify' it.
also instead of converting to a flat bar, you could convert to a bar like pic related, and then you won't have to change your stem, levers, or recable the bike. And you get to keep the retro look. Velo-orange sells them.