English Translation
I felt better to hear that.
I was relieved to hear that.
is a better translation to capture the nuance of ほっとする. You can find many example translations of “relieved to hear” in Japanese here on 英辞郎.
We spell it as ホッとする in the combination of Katakana and Hiragana more often than ほっとする in all Hiragana.
Also, 安心した (pron. あんしんした) is a complete synonym of ホッとした. Both ホッとする and 安心する have the connotation of “peaceful mind” or “calming DOWN” rather than “cheering UP”.
If you prefer a more formal expression, 安堵した (pron. あんどした) also works.