Well real busy like what? you cant even get about 1-2 hours a day? You kinda remind me of myself of those hectic days, bit i was  3-4 years younger then you, well now i am older than you. Well my friend you got 2 options

Option #1

Join any fitness club, ask one of the trainers for suggestions, he will give you adivce on what to eat more and what exercising machines you should use often. You can work out for about an hour and you will start feeling good within 2 months. I vouch you if you follow everything the right way you will get there after all this was exactly what i did.

Option#2

If you dont want to join fitness club then buy a pair of dumb bells (20-30 lbs which ever works for you) then go to some sports shop and buy Perfect Pushup device, now this is a rotating object you use while doing a pushup, this is a very handy device. And then go to one of the GNC and ask the cashier for Protein Shake wich is good for gaining volume of muscles or weight. If you do pushups as istructed on that Perfect pushup catalog and use dumb bells  in a efficient manner and eat Rice, sardines,Bacon(if you eat bacon), Wheat bread .

Since i dont go to the gym any more i do the option #2.When i first started to go to the gym i was about 123 lbs about your exact height, then i went up to 167lbs in  about 7 months(btw i was strict on my exercise and my meals), then later on i dropped to about 154lbs because i dont wanna be too big, now am all set