lost weight but flabby ,no muscle

ok 2 years ago when i left school at 16 i was 13 stone and then last month i was around 11 stone 6 pounds and now im 18 year old i weigh 10 stone 7 pounds at around 6ft and anyways i have obviously lost some weight recently and its been mainly through dieting and not alot of exersise and my exersise level i would say was sedentary to maybe light but im a thin frame and people say im thin but when i take my top off im little bit flabby in my chest area as in moobs there soft and pointy and also my stomach area and still have love handles and its very soft and when i sit down i have like a roll or 2 of fat and when i bend over its like a small pouch of fat that hangs over & when i stretch you can see my rib cage and my back is boney and stuff its just mainly my front like my chest area, stomach and love handles area that are flabby but i have no muscle and stuff and can easily grab the fat so do you think its because i have lost weight and muscle mass and that i should do strenth training and keep my healthy eating up as i think im skinny fat and maybe need to hit the weights as my weight on scale and BMI says im good weight but want to change the look from thin soft and flabby to thin and toned muscular look , some detailed advice would be great thanks sorry if it sounds confusing all this lol