It's not correct.
The subject "I" is usually omitted. If you say it, は is used for わたし since が unnecessarily emphasizes the meaning such like "I, not someone else, like...".
A translation of "ice cream" is ひょうか, not ひようか ("yo" must be the small one). However, the loan word アイスクリーム is far more common.
The -te form is not used for the structure "to like to do".
It's このむ, not こんむ, but another word is more commonly used for "to like" (hint: a na-adjective).