I used to play with jellyfish at the port when I was child.
I used to go to the port and play with jellyfish and poke them with my finger when I was a child.
「つつく」は「poke」という動詞になりますが、この場合は「poke」を別に使わなくてもいいと思います。
「小さい頃、浜辺で、くらげを指でつついて遊んでいました。」
I used to play with jellyfish at the port when I was child.という文章で大丈夫です。
「poke」という動詞を使いたいなら、下記の文章を使えます。
I used to go to the port and play with jellyfish and poke them with my finger when I was a child.
しかし、「I used to play with jellyfish at the port when I was child.」の方が自然です^^