if you're doing the lower-body exercises 3x a week, you have plenty of time to work your upper body. just alternate days (although, for my money, 3x a week is too much - i never did strength training for each body part more than 2x/wk bec the body needs at least 2 days betw workouts to allow for repair and rebuilding although, to be fair, i was using heavy weights at the gym).
if you only do pushups and planks, that's an entire upper body and core fitness routine, right there.
planks, obviously, you hold as long as you can and try to beat your time with each session.
pushups, work up to 15. if you can do 15 pushups in the plank position (not "lady" pushups), then it's time to intensify. you can do that by adding weight (put something on your back or wear a weighted vest or have your toddler sit on you) or you can slow it down - take a full steady count of ten to go down, hold in the down position for three, then count a steady ten on the way up, kinda thing.
just a little side note: you should know that once your body has caught up to it, 20 min three times a week really isn't going to do much at all for strength building. your body is a wickedly marvellous machine - it adapts fast and it likes to cheat, lol.