You need a solid, good routine to actually _see_ any gains in 3 months. But you can definitely feel gains in just a month or even sooner. And you weigh so little, I wouldn't worry too much about being strict about eating. Just make sure you get enough protein and don't eat crap all the time and you'll be fine. It doesn't kill you to go out for a pizza every once in a while with friends

Using myself as an example, I find it very hard to be absolutely strict about what I eat. If I feel the need to eat some pizza or nachos or something, I eat them but I make sure I stay below certain amount of calories. That way you don't have to worry about too much what you eat as long as you get enough protein and other nutrients.