The Gemara in Sanhedrin 94a says that the reason Chizkiyahu was not the Mashiach is that he didn't sing after Hashem did miracles for him (Rashi adds that this refers to saving Yerushalayim from Sancheriv and healing Chizkiyahu):
אמרה מדת הדין לפני הקב"ה רבש"ע ומה דוד מלך ישראל שאמר כמה שירות ותשבחות לפניך לא עשיתו משיח חזקיה שעשית לו כל הנסים הללו ולא אמר שירה לפניך תעשהו משיח לכך נסתתם
The attribute of justice said before the Holy One, Blessed be He: Master of the Universe, and if with regard to David, king of Israel, who recited several songs and praises before You, You did not designate him as the Messiah, then with regard to Hezekiah, for whom You performed all these miracles, delivering him from Sennacherib and healing his illness, and he did not recite praise before You, will You designate him as the Messiah? It is for that reason that the mem was closed, because there was an opportunity for redemption that was thwarted.
Yet we find in Yishayahu that Chizkiyahu seemingly does sing! (Isaiah 38:9-20). He even promises to sing to Hashem his whole life:
יְהוָ֖ה לְהוֹשִׁיעֵ֑נִי וּנְגִנוֹתַ֧י נְנַגֵּ֛ן כָּל־יְמֵ֥י חַיֵּ֖ינוּ עַל־בֵּ֥ית יְהוָֽה׃
“[It has pleased] the LORD to deliver us, That is why we offer up music All the days of our lives At the House of the LORD.”
Does anyone have a good resolution of these sources?