You could try any the modern warfare test ranges, cod 4 was my favourite. While doing so you could adjust your sensitivity in small increments up or down until you find what you're most comfortable with.
Practising against bots in ghosts while adjusting your sensitivity would probably work best since every title runs slightly different movement side for me personally.
To improve aim it's also a good idea to try and burst fire instead of just holding down the trigger full blast and guns are unique in the way they sway/recoil so finding a gun that works best for you will really help too.
Adjusting your perks to help with ads speed might help too if you ads a lot and in cqc knowing when to hipfire instead of ads'ing might not help your aim but it can help you get the drop on someone more efficiently.
Hope this helps and in this case, practice also really helps.
I was a noob to the COD Multiplayer before this game, so I can relate!
I think you've done the first thing correct by trying out Squads, I'd recommend stopping here for a while and just messing around with different guns and scopes. Try starting with the lower recoil weapons, SC2010 AR works well for me, you can also add a grip to these weapons if you're still having issues.
If you are struggling with flinch when you are getting hit, use the Focus Perk and see if that helps.
If this doesn't help, try altering the scroll speed of your controller, making your moves more delibrate and less likely to jerk.
I also learnt quite a bit about the maps and weapons by playing Squads 'Safeguard' mode.
Overall, practice makes perfect. There is no short cut, but there are tools to help you improve.
Hope this helps / you enjoy the game!
Here's a few basic tips that should help you improve your gaming experience...
You might want to grab a few friends and play WARZONE on the easiest tier then move up to the hardest mode or SURVIVAL prior to jumping in at the deep end (MP).
 Learn the maps.
 Try out all weapons until you find the one that your comfortable with.
 Communicate with fellow squad mates at all times or when you can.
 Have your aim sensitivity set at a low rating then move it up when your ready.
 Use cover when possible.
 Due to some weapons recoil it might best best to aim at there chest before unloading your mag.
 Try to have your enemy in your sight (ADS) before taking your shot and fire in short bursts.
 Take cover and reload in a safe area, not in the middle off the map whilst your foe has you in his sights.
 Flank... always flank no matter the size off the map or what game mode your playing, this will keep you alive longer and hopefully get the drop on someone.
 Run with your fellow squad mates, two people firing at one enemy will take him down quicker, it's not about getting the highest K/D/R it's about winning the current game your in at that time.
 Learn from your errors and practice what needs your attention.
Now on to PERKS...
Different perks as you know will give you various advantages etc, try them all, again, find what works for you, remember different maps= different weapons/perks and so forth.
Start with the easier items i.e "Sat Com/Guard Dog/IMS" then you can consider aiming for the others'... Battle Hind/Gryphon etc
What ever you do, have fun buddy it's a game, granted some folks take it seriously usually the "Pro" gamers that's cool with me and hats off to them.