1. Ability Scores
When you're optimizing a specific build, you should start with a goal on what this build should accomplish. From your question, you have already stated that this goal is damage dealing as a two-weapon fighting Eldritch Knight. First, let's look at your stats.
STR: 17 (+3), DEX: 18 (+4), CON: 16 (+3), INT: 15 (+2), WIS: 11 (+0), CHR: 11 (+0)
You have high stats in both Str and Dex, while you will only use one of them. You need to choose which one you will use instead of increasing both. The main two differences in terms of optimization is AC and damage when deciding stats. If you go Str-based, you're able to use heavy armor, and you can use longswords and other equivalents (like the battleaxe) if you take the Dual Wielder feat later, also other finesse weapons. If you opt to go Dex-based, you can better utilize light armor, and you can only use rapiers if you take the Dual Wielder feat later.
I suggest you switch your Str score and your Int score, and max Dexterity as soon as possible. My suggestion is to go Dex-based for several reasons: no stealth disadvantage, ranged options, and initiative. You can better utilize your current Str score of 17 for your Int score instead. Int is used by Eldritch Knights for spell attack modifiers and spell save DC. If you rather choose to go Str-based, give the 18 to Str, and the 17 to Int. Also, you're a fighter first, so max out your main attacking ability score first before you do your Int score.
2. Fighting Style
You have a 17 in Str and an 18 in Dex, you use two scimitars for now, and you have the Great Weapon Fighter fighting style. At level 5, you can make two attacks with your action and one with your bonus action, with the following calculations (assuming all hit):
Action: 2 x (1d6 + 4) = 15
Total: 18.5 DPR
Right now we can see that your current fighting style does not benefit any of these attacks. At all. If you want to use two weapon fighting, I suggest you take the Two Weapon Fighting fighting style instead, which lets you add your Str or Dex bonus to the bonus action attack, resulting in 22.5 DPR with your current stats.
3. The Dual Wielder Feat
You might be considering this right now, and this is a good feat for what you're going for, a natural progression of your build. However, it is better to max out your attacking ability score first before you take this feat.
4. War Magic
This is where it all breaks down, unfortunately. The answers above is assuming that you are set on being a two weapon fighting Eldritch Knight. However, the subclass feature of the Eldritch Knight that you will get at level 7 clashes with two weapon fighting. Let's take a look at what it says.
When you use your action to cast a cantrip, you can make one weapon attack as a bonus action.
First off, let's calculate some damage again to see if it's better to use a weapon cantrip (Booming Blade, Green-Flame Blade) or just use two attacks with your scimitar at level 7 (I'm assuming you will max out Dex at level 6).
1d6 + 1d8 + 5 = 13 DPR
2 x (1d6 + 5) = 17 DPR
As you can see, a cantrip will only outdamage your attacks if you can trigger its secondary effects; with Booming Blade it's an additional 9 (2d8) damage and with Green-Flame Blade it's 7.5 (1d8 + 3) if your Int is at least a 16. Further reading here.
What does this have to do with War Magic? Well, War Magic allows you to use this bonus action attack with any weapon, including greatswords and halberds. So, there is no need for you to use two weapon fighting if you're optimizing for damage as an Eldritch Knight. Hell, even going with just one scimitar can net you more damage with the Dueling fighting style, and it's all because of War Magic's action economy.
My suggestion is to evaluate what you want out of this build. It's completely, 100%, fine if you want to go two-weapon fighting for the sheer cool factor of it, even if it is suboptimal from level 7. But if you want damage, my personal suggestion is to use the halberd/glaive so you can kite your target with booming blade and then move away. Others might suggest a greatsword and take the Great Weapon Fighting feat, however the -5/+10 thing have lower returns on your DPR the more damage you do in a single hit before you take the -5/+10 (which you will have more damage because of the cantrips).
Other options for two weapon fighting
I know you said that you wanted to stay an Eldritch Knight. That's fine. I just want to quickly mention that Rangers make excellent two weapon fighters, and they get access to spellcasting. And with two weapon fighting, they can really utilize the Hunter's Mark spell. Although it needs to be pointed out that the spell itself might clash with your bonus action economy, so your mileage may vary.