Bra Alternative? Iron fusible fabric on inside of shirt? Sewing Machines Parts and Sales in Los Angeles

I don’t wear bras and always have a “reveal” nipple problem, now that clothes are being made thinner. I was thinking of ironing on fusible cloth or patches on the underside of my shirts. I’m tired of putting uncomfortable underclothes/patches/pads on my body. I rather alter my shirts slightly thicker. Does this sound like a reasonable solution?