ついていきます

will follow

→ 付く
phrase Rare #37,768
will follow Polite form of ついていく, used when saying that you will follow or accompany someone. It can also mean going along behind someone or keeping up with them.
JA: 私も一緒についていきます。
EN: I’ll come along with you too.

私は後からついていきます

I'll follow along afterward.

たとえの中水の中あなたにならばどこまでもついていきます

I’ll follow you anywhere, through fire and water.