Great for you Joey! Adding some jogging would help you loose weight, but take your time, it's better to get yourself in the habit of exercising and slowly building on more activities than suddenly doing a lot of activities and burning out, and eventually quitting.
You'll feel better by the end of June if you stick with it.

Though, if you're working out properly, no matter how fit you are, you'll be bound to feel sore on some days after some workouts. If you never feel sore, you're either extremely lucky genetically or you're not getting any more fit.