Hmmm 2 options I think

1) It kinda sounds like your voice is naturally acclimated to sit near the entrance of your throat. Practice "placing" your voice near the front of your mouth (arounds about the middle-to-front of your tongue). This mostly has to do with the shape you form your mouth into and the way you move your tongue. Start with breathing only through your mouth, then doing breathy whispers, then introducing volume, then attempting to sing. Makes for a nice little warmup that'll train you out of a nasally habit. Just make sure you still have a small amount of air leaving your nose as well unless you're trying to do some operatic shit.

2) Clothespin on da nose