Name spelling (opinions please)

Chelsea • My sweet hubby and I have been together since 2009. Our sweet Madilyn Ann born 11/5/16! We`re finally complete!
I'm having a sweet little girl! My hubby and I decided on (and love) the name Madilyn! I know the traditional spelling is Madelyn or Madeline.. But I personally don't care for those spellings. So her name will be Madilyn Ann and we will call her Maddie for short. Now comes the part where I need opinions.. A friend of mine pointed out that it looks odd and isn't "grammatically correct" to spell the shortened version of her name "Maddie" since her full name is spelled "Madilyn".. Said it should be "Madi" but I don't think "Madi" looks right. Now I'm stuck and second guessing spelling and everything. And I'm sure my mama brain is over thinking everything. I just want opinions. Does it look bad or is it ridiculous to spell her full name "Madilyn" and spell the shortened version "Maddie"?