The muscle pain you describe is normal (DOMS or delayed onset muscle soreness), and it is often worse a couple days after an intense workout than the day right after. If you are like me, you are stiff and something as simple as walking up a step 'hurts.' Strangely, I love feeling this kind of muscle soreness, and if I don't feel it after a workout, I tend to think I didn't work hard enough. (This is not scientifically true, but it's just a head game I play with myself) I know it can seem impossible to do the same exercise, but once you start moving, something happens, IDK, maybe muscles "warm up" or something, and then you can do more.
I try to do body pump (group weightlifting classes) on Monday and Wednesday evenings, and Wednesday evenings I often go in very very sore, but I always leave feeling good. And then hurt the next couple days, but like I said, I like it... I have been a moderate exerciser and try for 2-3 times a week. I do not consider myself skinny even though I need a size 00 or 0, but I am very short, only 4'11" (okay, I rounded up a half inch...) and I usually weigh about 97 pounds. I am not the fittest person in the world, but I am reasonably fit and I think relatively strong for my size. In body pump class I routinely lift as much as women 1.5 times my size. I can probably bang out 15-20 push ups on my toes, and I can hold a plank long enough to get very bored.
It sounds like I eat waaay more than you, though. Your diet seems to be very lacking in fats, and that can be a problem. Maybe you should try to eat some nuts or something to increase your caloric intake. I think I probably eat 1,400-1,800 calories a day.
You cannot gain muscle if you do not work them to exhaustion, I think. Something about microscopic tears in muscle fibers after working them and the necessary repairs your body will do to fix them is what actually builds muscle.
When I am at my fittest, my body tends to naturally want to eat more. I've never had a problem with weight but my body composition will change if I'm not working out.
You can find body pump classes on youtube because future instructors record audition tapes and put them up. Try to do one without weights and work your way up to some small dumbbells. I am a lover of weight bearing exercises and not so into cardio, though.