Welcome to Stack, and tabletop gaming! You do have a few glaring issues in your character, which I'll do my best to help with.
Background is not something freeform that you write yourself. I mean, I guess you could do that, but you will be losing several important increases to your character and playing an overall less powerful character if you do.
The backgrounds given in the rulebooks also provide your character with proficiency, specific roleplay opportunities, and sometimes even new abilities. Point being, they give a mechanical advantage as well, not just a general backstory for your character.
To address the concern of your character's Background not matching their personal history, that's something you can chat about with your DM. Your DM should be flexible on what the Background actually entails for your character's history, and I've never met one that strictly expected people to play a literal textbook version of their character's personality.
Something is off, as you have a starting strength of 19, which should not be possible under any method as a Tabaxi. The absolute highest you could have is 18 if using the dice roll method.
If you did use the roll method (your post is unclear, but you mention that a stat "rolled" as something multiple times), unless you were given permission by your DM, they will want the dice rolled in front of them, not on your own, to prevent cheesing/cheating.
Saving throw proficiency does not add your proficiency bonus to any rolls for that stat. It only adds proficiency to those saving throws. All other rolls are unaffected by proficiency to saving throws.
Something is off here as well; you don't have as many proficiency as you should, and you have one that isn't possible for you to have. When creating your character, you get skill proficiency from three sources:
Class. When creating a Fighter, you can pick two from Acrobatics, Animal Handling, Athletics, History, Insight, Intimidation, Perception, and Survival.
Race. Being Tabaxi gives you proficiency in the Perception and Stealth skills.
Background. You didn't pick one, so you don't have those. This is another reason why Background is important beyond the character's history, and why it is necessary to select one.
Arcana is not an option for you (though it could be, depending on Background), so you have no way to have selected that Skill. Additionally, you should always have Perception and Stealth as a Tabaxi racial, and you have neither.
Armor does not apply your proficiency bonus to it. Proficiency in armor simply allows you to wear it.
"10 + Dex bonus" only applies to being nude or wearing regular clothing; it does not work if you are wearing any armor.
How your AC is calculated depends on which armor type you are wearing. Light armor is the armor AC + dexterity bonus. Medium armor is Armor AC + dexterity bonus (max of +2). Heavy armor is simply Armor AC, no bonus from dexterity.
In your given example, if given Plate armor and a shield, your character would be at 20 AC. 18 base AC from the armor, gains +2 from wielding a shield as well. You would, additionally, have disadvantage on all Stealth rolls, so that may or may not be worth it to you or how you want to play your character.
Is your AC a bit high with Plate as a level 1? Perhaps; but that is why it isn't possible to start with it. You would have to earn it in game somehow, and overall, it isn't absurdly high. Yes, you're hard to hit if you gear yourself as the tanky type, which is exactly how it should be. It wouldn't be fun to be the tanky armor wearing type if you were easy to hit!