First, congratulations on recognizing a potential problem, and starting to take steps about it while you are still young. Building a lifetime of fitness habits is much easier to do starting at your age.
A few things that I would point out that may help. As others have stated, muscle weighs more than fat, so if you swap out the same amount of fat mass for muscle mass, overall you will weigh more.
For the fitness and eating, there are a few red flags, which I'll outline.
- No plan - You're doing "some sit squats", some random things you found on the internet, and a few planks here and there. It's having a small effect, but towards what? You need to define some goals. Short (6 month), medium (6 mos to 2 years) and long term (longer than 2 years) type goals. Then come up with a complete, well rounded overall body workout plan geared towards those goals. Without a plan, you'll just kind of lumber around doing stuff and wondering why it's not really working. Figure out that goal, and the other planning will be easier.
- No eating plan - Note I don't say diet. A diet is a short term thing, usually abandoned after the initial success wears off. An eating plan is persistent, long term habits designed to ensure the success of your fitness plan (See note #1). For weight loss, you simply need burn off more calories than you eat. Take a look at your fitness/weight plan, and see how your diet really stacks up. There are tons of calculators around, use them as a starting point but realize that you may need to adjust up or down, since they are all just educated guesses.
- Keep a diary/logs - Wondering why you gain weight in the spring? Or why you seem to always feel droopy by Thursday? You can't know what might be causing it, if you don't track the history. Also, until you REALLY know how many calories are in the various foods you eat, keeping a food diary/log religiously can be very enlightening as to how many calories you're really eating. This can include borrowing or buying a food scale. You'd be astonished at what actually constitutes a serving vs how much your probably eating.
Now, a few caveats and things to think about.
Find an activity/exercise that you really enjoy. If you don't enjoy what you're doing, it will be difficult to maintain it for the long term. Too many times people join a gym, find out it's hard work and that they don't really like going to the gym, and they'd rather go ride a bike. Great! Go ride the bike. Just find something that you can do that you enjoy and will also provide the fitness benefits you are looking for. If it's not a full body exercise, figure out what you can supplement with.
Same thing with your eating plan. If you really like eating Paleo, or China Study, or whatever, then fine. As long as it meets your workout needs and you enjoy the foods, have at it. Just keep that diary, because you can overeat on the good stuff just as easily as junk. Don't base a plan on deprivation, just remember that if you have that bowl of ice cream with chocolate syrup and sprinkles, you've got to accommodate it in your calorie count.
Looking at the scale over a month is short term. Weight can fluctuate by a few pounds up and down in a day. Weigh yourself at the same time under the same conditions, and look at long term trends. Don't really obsess over what you weighed yesterday, or what you weighed last week. Worry about what you're going to weigh in 6 months or a year. Use the little steps to build towards the big ones, and if you gain a little one week, don't beat yourself up. Weight loss is a marathon, not a sprint.
At 16 years old, you may still be growing. Weight and other things may fluctuate over the next few years, just remember that and keep your eye on the end goal. It's absolutely wonderful that you are starting this, but doing it correctly from the beginning will save you time, get you closer to where you want to be, and minimize the chance you'll quit or have to try to erase bad habits later.