Do that. Start small. Just work yourself up gradually.
I have always had a hard time carving time out of my day to exercise. I'd do it for a while and then kind of slack off when things got busy or I got distracted.
That's why I had to work it into my regular schedule. I got a bike specifically to force myself to get some daily exercise (as I've already explained
elsewhere), so if you can figure out some way to put more exercise into your daily routine, do it. It can only help.
Also: modify your diet. Building muscle takes materials. Think about increasing your protein, whether from animal or vegetable sources. Also keep an eye on your vitamins; taking a daily chewable or something might be a good idea. I'm not worried about you eating, as you seem to much a lot, but you do need to be sure you're getting the right KIND of nutrients to help your body build the muscle you want it to.
Also, if you're that skinny? You've got room not to worry about fats and calories. Too much sugar and chemicals doesn't do anyone any good, but you don't have to worry about eating light, just eat solid, protein-rich foods to give your muscles what they need to develop and your body the energy it needs to keep using those new muscles.
That's about the only advice I can think of right now. You might consider asking some advice specifically from
sevenpercentsolution; she's done this kind of training professionally, I think. Or semi-pro. Regardless, she's a good person to know, and she has solid knowledge of this kind of business.