You have several options to increase your AC.

Spells

Shield will increase your AC by 5 for a round and it's a life saver if you suddenly get swarmed. Though if you are not careful it can quickly eat through your few spell slots.

Mage armor will set your AC to 13+Dex if you are not wearing armor. It is of no use to a Draconic Bloodline Sorcerer, but it's worth listing for the sake of other sorcerers.

Honorable to mention blur and mirror image. Although neither increases your AC they both make you much harder to hit. Mirror image doesn't even require concentration.

Racial Traits

Beasthide Shifters from ERLW gain a +1 bonus to AC when they use their Shifting trait.

Githyanki from MTF have light and medium armor (but not shield) proficiency through their Martial Prodigy trait.

Githzerai from MTF can cast shield once per long rest starting at level 3 through their Githzerai Psionics trait.

Hobgoblin from VGM have light armor proficiency through their Martial Training trait. It is of little use to a Draconic Sorcerer, but it's worth listing for the sake of other sorcers.

Lizardfolk from VGM have AC equal to 13+Dex through thier Natural Armor trait. It is of no use to a Draconic Bloodline Sorcerer, but it's worth listing for the sake of other sorcerers.

Mark of Sentinel Humans from ERLW can cast shield once per long rest through their Guardian's Shield trait and add shield of faith to their spell list through their Spells of the Mark trait.

Mountain Dwarfs from PHB have light and medium armor (but not shield) proficiency through their Dwarven Armor Training trait.

Tortles from TTP have AC equal to 17 through their Natural Armor trait. That just speaks for itself.

Loxodons from GGR have AC equal to 12+Con through their Natural Armor trait. At first glance this seems less than 13+Dex, but being able to scale both your AC and HP simultaneously with Con, while disregarding Dex can make you quite tanky.

Simic Hybrids from GGR can gain a +1 bonus to AC while not wearing heavy armor at level 5 through their Natural Enhancement trait.

Warforged from ERLW have +1 bonus to AC thanks to their Integrated Protection trait.

^{For races that appear in multiple books, I only mention their first official publication.}

Armor and shield

If you want heavy armor and shield, you will have to multiclass, the typical choices being a dip into either Fighter (which has to be your first level, but also gives you the Defense Fighting Style) or Clerics of certain domains.

For medium armor and shield you have a greater variety of choices.
On one hand, you could multiclass, the typical choices being again a dip into Fighter or Cleric.
On the other hand, you could get the Moderately Armored feat at level 4. However, to take that feat you need to have proficiency in light armor, which you could acquire from your race: Githyanki for their Martial Prodigy trait, Variant Human to start with the Lightly Armored feat, Hobgoblin for their Martial Training trait, and Mountain Dwarf for their Dwarven Armor Training trait.

What to choose

Each of these options come with costs, so which you choose depends on what you want to prioritize:

• Sorcerers have few spells known, so you may not want to learn too many defensive spells, but I really recommend taking shield regardless of any other choice you make.
• None of the playable races I have mentioned will boost your charisma, with the exception of an optional +1 from Variant Human, Simic Hybrid, or Warforged.
• Taking the Medium Armor feat will leave you relatively vulnerable at level 3 and will replace your Charisma increase at level 4. Moreover, although I personally prefer the Medium Armor feat I do not think it is a good option for you because it works best if the Dex is 13, which is impossible in your case.
• Dipping into a fighter will delay all your sorcerer features, while dipping into Cleric will delay all your sorcerer features except for the number of spell slots.

In your case, because your stats are all very high and you don't have to worry about being MAD, I think that dipping Cleric with a domain that grants heavy armor is the most effective option. You could do just fine with any race, but to maximise the AC further I would pick the Warforged.

In my experience playing and running D&D, unless you have an unusually high number of spellcasting enemies, this won't actually be that big of a deal — your once-per-short-rest-advantage feature should cover it. (You might want to move it down from 11th level, maybe starting with once per long rest.)

But, I also want to challenge one of your statements. You say that the secondary abilities and save proficiencies can't be changed for flavor reasons. I buy that for the secondary abilities, but I think you could reconsider this for saves. A lot of the "secondary" saving throw proficiences in the core classes are not particularly thematic — notably, Int for druids, Cha for clerics, and arguably Con for sorcerers. They're not unreasonable, but don't deeply tie to the class overall.

So, I wouldn't blink at making the saving throw proficiencies for your subclasses not align with the secondary ability scores for those subclasses.