Is it possible to learn a second language and speak it perfectly?

im 14 and have been studying french for almost 3 years, italian for 2, and im starting arabic soon. Ive been told my french pronunciation is very good (as is my italian) but i always am self concious to speak it because i fear i will sound like a nasally ignorant american. with studying and immersion is it every truley possible to have native like speaking?