I cared about the grammar too much and I couldn't speak smoothly.
I concentrated(focused) on the grammar too much and I wasn't able to speak smoothly.
「文法を気にしすぎてたらうまく話せなくなってきました」
I cared too much about the grammar and I couldn't speak smoothly.
「気にする」はcare about~と言い、「気にしすぎ」はcare about ~ too muchとなります。
「うまく話せる」はcan speak smoothlyと言い、この例文では過去形の否定文になっています。
couldn't speak smoothlyのcouldn'tをwasn't able toに変えて使うこともできます。
例) I couldn't speak smoothly. --> I wasn't able to speak smoothly.
また、例文の前半にはI concentrated(focused) on the grammar too much(文法に集中しすぎた)という言い方も使えます。