I think I should stay on the safe side and not exert myself too much for about two months or so until I get better.
ご質問ありがとうございます。
"I think I should stay on the safe side"＝「大事をとって」
（又は、"I don't think I should take any risks for now"＝「今はあまり危険になることはしない方が良いと思う」とも言えます。）
"and not exert myself too much for about two months or so"＝「二か月間ほどは無理をしないようにします」
"until I get better."＝「体調が良くなるまで。」
ご参考までに。
I think it might be better for me not to push myself too hard until I'm completely better.
I don't think I should do too much for the next couple months just to be on the safe side.
この場合、次のような言い方ができますよ。
ーI think it might be better for me not to push myself too hard until I'm completely better.
「完全に良くなるまで、あまり無理しない方が良いみたい」
not to push oneself too hard で「あまり無理をしない」
ーI don't think I should do too much for the next couple months just to be on the safe side.
「大事をとって２ヶ月ほどおとなしくしていた方が良さそう」
just to be on the safe side で「大事をとって」
ご参考まで！
アメリカ合衆国 
カナダ 
