I think he probably had this skin disease from before, but just didn't show any symptoms the last ten days.
この場合、次のような言い方ができますよ。
ーI think he probably had this skin disease from before, but just didn't show any symptoms the last ten days.
「彼は多分元々皮膚病を持っていたんだと思うけど、この10日間症状が出なかったんだ」
he probably had this skin disease from before「彼は前から皮膚病があったのかもしれない」
to not show any symptoms で「症状が現れない」
ご参考まで!