Elle,
You mustn't inject into fatty deposits as it seriously messes with the rate at which the insulin is absorbed.
Are you changing your needle with each injection? I used to think that that was a bit over the top but have been persuaded by my DN to do that; so I'd make sure you do it too. Needles are designed for one use only and so it makes sense really to follow their intended design.
Use your bum, your upper arms, your legs and rotate through all of them. Avoid your stomach for a few months until those fatty deposits go away. I hardly have any fat on my thighs, but that is fine for injecting. You'll find different areas will have slightly different absorption times for insulin so you may want to keep an eye on blood sugars if you do change.
It's not just the issue of looking unsightly; like I said it can really have a bad effect on your control.
Good luck with the low carbing; I think it is the best way of achieving good control for any diabetic, Type 1 or Type 2.
Best
Dillinger