I completely understand your apprehension, and I was a bit wary of injecting in public too, but no one really notices.
Earlier today, I injected sitting on a park bench. I just did it casually and I don't think no one even noticed.
I was advised by my team to never inject in toilets since they're not sanitary. They said if a restaurant asked me not to do it at the table (but really, but they time they saw what I was doing and said something to me, I'd be done), I should ask to use somewhere like their staff room, but definitely not the toilet. Asking someone to use the toilets to inject would be like asking someone to feed a baby in the toilets.