I have a lot of thick hair, so I can only do certain hair styles.
I have a lot of thick hair, so my hair styles are limited.
ご質問ありがとうございます。
上記の英文では2番目が元々の日本語を直訳しています。完璧な英文ですが、1番目の方が自然な言い方だと思います。
「髪が多くて太い」はI have a lot of hair that is thickとかI have a lot of thick hairとかI have a lot of hair and it's thickなどに訳せますが、I have a lot of thick hairではすっきりとした英文ができると思います。
ご参考いただければ幸いです。
My hair is thick and heavy, so my hairstyle options are limited.
My hair is thick and heavy, so my hairstyle options are limited.
I have a lot of thick hair, so I can’t do many hairstyles.
Because my hair is so thick, it’s hard to style, so I’m kind of limited.
「髪が多い」は英語だと I have a lot of hair / I have really thick hair のどちらでも言えますが、日本語の「多い＋太い」のニュアンスは “thick and heavy” がとても近いです。
アメリカ合衆国 
