I've seen people say that playing on a smaller screen will make you better, and while that may be true, it's not why you're playing poorly. I play on a 65" TV and what's more important is my seating situation in relation to the TV. If you have to play on a larger screen, sit in a sport where you can see the entire screen without having to move your eyes around too much.
Learning the game and controls is the hard part. The maps are different, but as you play you'll start to see patterns where people tend to flock. Use that to your advantage by being there first or flank them and pop up from behind.
I'd also look at the aim sensitivity. I have mine at the highest setting, where as others use the lower settings. Experiment and find what's comfortable for you.
For Call of Duty, the weapons and perks you use can dictate your style of play. Keep all of that in mind when you're building your loadout.
It's also important to stick with a weapon or two, instead of trying everything - at least while you're starting out. You'll become more comfortable with the rate of fire, optics and time to kill. You'll learn when you can and should start shooting, rather than wasting ammo trying to get long shots.