Both two sentences are correct. There are few differences between those two forms. "鼓劲" is more likely followed "加油"，that is "为某人鼓劲加油", but "鼓励" can not. Chinese use "鼓劲" usually during a game or an activity, but use "鼓励" more widely and more often. e.g. if someone failed in business, we would "鼓励他不要气馁"。

If you want to say "encourage someone" in Madrain, you can say“鼓励某人” or “为某人鼓劲”. So the difference lies in their collocations.

鼓励，Transitive verb 鼓劲，intransitive verb 鼓励，使用频率更高