Yes that can happen. I have known people who were tubby and plain but after puberty they lost the puppy fat and became very handsome or pretty.

Yes it's well known people that are beautiful in puberty/ teens become ugly in their 20's/30's...and those ugly as puberty teens become beautiful for 20's/30'/40's. 

Generally the beautiful teens are peaking as teens...age 20 on it's usually all downhill for them. Generally the opposite is true of ugly teens from age 21 on it's all uphill for them in terms of looks.   

You get a different perspective most certainly

I've been told more than once that I was a late bloomer, so I believe you can.

There is truth in the story about the ugly duckling.

Tons of people are late bloomers. But I wouldn't worry if I were you. You're not as ugly as you might think.  Stop worrying !