上がる!

My school improved its grade!*
私の学校は上がるです。

1. 私の学校の評価は上がりました。（The reputation of my school improved）

（This should be past tense）

My principal is proud.
私の校長（先生）は得意気です。

（adding 先生 would be more polite. I recommend you always add 先生）

*Schools are graded on an A-F scale. We went from an F to a C. (F being the worst grade to A being the best)

よくできました！

Keep up the good work!

上がる!

My school improved its grade!*
私の学校の評価がは上がりるでます。(*評価[ひょうか])

(I think what you wanted to say was "your school is put a higher value" or "they holds a good opinion of your school". If it's not so, please tell me.) 

My principal is proud.
私の校長(先生)は得意気です。(In this case, I would say 校長先生は(そのことを)誇らしく思っています / 誇りに思っています。*誇らしく[ほこらしく]、誇り[ほこり])

*Schools are graded on an A-F scale. We went from an F to a C. (F being the worst grade to A being the best)

Good job and congrats for your school! Anyway, I hope this helps you.