Pinch your nose and read a paragraph. Notice if your voice sounds more nasal than normal. If it does, then your singing voice is naturally nasal. The key is to control how open your throat is as you speak and sing.
Use a voice recorder to record your reading while pinching your nose.
Play back your recording and take note of when your voice sounds more or less nasal. This will show you where you need to focus and which sounds are tripping you up.
Practice reading with the voice recorder until you're happier with the sounds you are making. Translate your new way of breathing and speaking into your singing practice.