First, I should express my thanks to my parents.They not only gave me
life (or 'brought me into this world'), but also taught me how to become a better girl. (Become a better girl is a bit 'Chinglish' Maybe 'they taught me to become the best person I can') Second, I should thank my
sister, she helps me without expecting anything in return. Finally, I must also express my thanks to my lover. (Lover is not normally used, it can mean the boyfriend/girlfriend of someone who is already married! Better to use husband/boyfriend/partner)
He made me realise how wonderful the world is.
I would normally use firstly, secondly rather than first, second but both are ok. The last one should be 'finally'. In this type of writing I would avoid carrying on with thirdly, fourthly etc. That makes it too much like a list.
非常好, keep writing!