No, it isn't wrong for you to sing in falsetto. Men have been singing in this voice for centuries, and it worked for the Beach Boys and Daniel Beddingfield.
But you need to choose the right repertoire (not girls' songs) and be aware of the possible problems that you might have singing in a voice quality that can dry your vocal folds.
As a young man, you need also to work with and make friends with your more usual male voice. After all, you are using it to speak in all day and it is a major part of your indentity personally as well as artistically.
If you find you don't have the range for the songs you want to sing, that is quite normal for a settling voice, and your voice may still be settling down after voice change at puberty. In the most drastic part of voice change the male singer is left with a narrow range of about an octave and a note, and it's quite challenging to find songs with that range, but it can and has been done. Transpose everything down until it fits your voice, don't try to strain and get notes that don't work well.
You need to find a good teacher to help you with this - you could do it alone but it would take longer and be riskier I should think.