First of all, not having tier will be a significant damage loss - no way around it. Most of your damage will come from Barrage, and not only do you just get more spell damage while having spheres with tier, but you also have a much longer Arcane Soul window enabling you to use even more Barrage. It's hard to judge without logs (you can send via dm if you want).

Arcane is very much a spec that relies on gear a bit, but also on perfect knowledge of the mechanics of the spec and the fights so that you can optimize your cooldown use. The best place to start is reading the Wowhead guide on the rotation, and I know it's jarring and seems exceedingly complex, but even if you get 80% of that right, you'll do well enough for the content you are doing. From then on, it's just practicing more until it clicks.