I am 5ft 8 and I have a small chest and waist, so I have to buy clothes in the boy's department since these are the only sizes that will fit me. I like taking off my shirt on warm days but only at the beach or near water because in any other public place, I worry about what someone will say if I am seen
5'8"? Heck I'm only an 1.5" taller than you. How much do you weigh? I was very skinny at 145Lbs at 5'9" in middle school. Like usual, eat more and work out, the older you get, the harder it will be. How many push ups can you do? You have to start somewhere.
You are what you are. There's no point being embarrassed about it. Work out hard, lift heavy weights regularly, get a trainer if you want even - make sure you eat loads of protein. I mean loads. You can always improve your body so there's no point being embarrassed about it. Change it!
If you want to change this all you have to do is eat more and work out.