Your situation reminds me of the one with my recent ex... i too live in Scotland, whereas she was across in Canada. It sounds like your lady is further west than mine as there was only a 5 hour difference between us.
I say only 5 hours but really... it was still a hassle when you wanted to talk to her for any meaningful length of time.
I can also empathise with your feelings regarding trusting those around her... my ex was a beautiful girl and she worked in a very male-dominated environment. None of them took her relationship with me very seriously and they frequently tried to encourage her to dump me or go out with them anyway. Sometimes she confessed to me that she was lonely and that made me feel guilty as well as insecure. Meanwhile over time her friends became ever more bothered about the idea of her leaving Canada to live with me (that was the plan) so they too became an issue. She used to tell me about their encouraging her to date local men (behind my back) and her refusals. Over time they kept demanding more of her time at my expense too. I trusted my ex absolutely so i knew she'd do none of these things, but the fact i couldn't trust these people played with my head too. So i know exactly what you mean in that regard.
I would say from my own experience that if she's gone to all the hassle of getting a visa so she could live with you, then actually gone through with it, then she must be really committed to you.
Mine talked about the visa step but never actually ever got round to it (she stuck to 2 week trips at a time). So i know from prior conversations that the visa she got isn't easy. If i were you i would take heart from her endeavours.
Sadly, i can also empathise with your feeling that you're slowly wearing your girlfriend down... you love them so much, so when things play with your head they take on so much more weight, which affects your girlfriend and weighs her down which in turn makes you more worried, anxious, keen to keep her and thereby playing with your head even more in a vicious cycle.
As Cuch says, long distance can be very hard and sadly even with a solid loving relationship the odds are difficult to overcome. They can be overcome, don't get me wrong.
Its just very difficult. Frequent visits are a must, i agree there too. Over time my ex began to value her job more and made less effort to get time off so we could be together. Her career back in Canada was eventually another priority that came before us. Sadly, another thing about long distance relationship is that over time one person's priorities can change and that can spell doom for the relationship.
But i'd say it sounds like things are going well for you here... my advice for now would be to stand back from your fears, relax, and just appreciate the fact that your girlfriend has done so much in order to be with you. Not anyone else - YOU.
So you are worth the effort and all the late nights in her mind.