He doesn't have anyone to talk to; so he just keeps it hidden inside himself.
「彼は誰にも相談できず1人で抱え込んでしまう」は、
He doesn't have anyone to talk to; so he just keeps it hidden inside himself.
でどうでしょうか?
※ keep ~ inside ~を自分の胸の中にしまっておく
※ hidden 隠された
ご希望の文に続けるのでしたら、少し変えて以下のような感じをオススメします。
He doesn't have anyone to talk to; so he just keeps it hidden inside himself. As such, he is overwhelmed and just stays at home.
※ as such そのようにして
※ be overwhelmed 打ちのめされる