I had the same test done when I was 3 for recurring UTIs. I do remember it because yes, it's unpleasant, but I wasn't "scarred" from it. It'll just fade into her memory, along with things like having blood drawn, getting stitches and having teeth filled - not pleasant, but necessary to maintain health and not traumatic.
Anyway...I don't think they found a smoking gun that explained the infections so I was put on a preventative dose of Bactrim (sulfamethoxazole or something like that is the generic) for several years. I outgrew the bactrim by the time I was in elementary school and had a few occasional UTIs throughout later childhood, then they came raring back when I became sexually active later on. I did have the VCUG repeated when I was in college to rule out anything that could have benefited from surgery. There was nothing, so I was on antibiotics for a long time again and eventually things settled down and I only get one every year or so now if I don't pee after intercourse (TMI, right)?
Some of us are just more susceptible to these than others. There are probably other preventative measures that you can take if they rule out reflux or any anatomical problems. Concentrated cranberry really does help support kidney and bladder health so that might be an option.
Don't beat yourself up over this - I remember that my mom was more upset by this than I was (she had to leave the room at one point). Your little girl will be fine!