All humans experience anxiety, and little ones experience it more than adults because they have more reasons to feel fearful in their daily lives. Humans seem designed to manage anxiety by giggling, physical activity, crying, "working out" the anxiety through play, and/or telling a story about the anxiety-producing event.
Sometimes children stumble on other ways to manage their anxiety, and one of those is Selective Mutism. So it doesn't necessarily mean that your daughter is more anxious than other children, just that she has developed a different strategy to manage her anxiety. The problem with this strategy is that it creates more problems. Young children are expected by their teachers and peers to engage verbally. They need to talk to be accepted and to function in school. So it's not an adaptive strategy.
It sounds like you're wondering if your daughter's behavior should really be diagnosed as Selective Mutism. I obviously can't diagnose her without meeting her, but if a developmental pediatrician diagnosed her, then it is likely she fits the criteria. This diagnosis does not mean that she NEVER speaks outside the home, just that she "consistently" elects not to do so in certain situations in which she is expected to do so. There is often a family history of social anxiety, although not always, and this is generally thought to be genetic in origin.
The fact that your daughter frequently complains of stomach aches and being tired suggests that she IS feeling anxious but does not know how to express it. Frankly, never having had any separation anxiety at all is unusual. It might indicate that she does not always feel comfortable acknowledging and directly expressing her fears and worries, and instead pushes them into her body, where she feels them in her stomach, or as tiredness, or as an inability to speak, or as needing to chew. This somaticizing is a pattern you want to interrupt, even aside from the selective mutism issue.
There was a time when kids with Selective Mutism were viewed as if they were "choosing" not to speak and were treated with behavior mod techniques and pressured to speak. Unfortunately, that just makes kids more anxious, so this is not an approach you want to take.
Now that this is understood as an anxiety disorder, intervention aims to help kids become more comfortable with their feelings, including their worries, fears and needs. The child learns healthier strategies to name, express and manage her feelings so she doesn't need to "stuff" her anxiety. Parents are supported to work with their child to manage anxiety and build her comfort level in social situations.
Many child psychologists do not have experience with Selective Mutism. It is my opinion that your child needs intervention from a professional who is experienced with this specific disorder. Ask the psychologist what their methodology is, and what their success rate is. You want to hear that they understand this as anxiety, rather than as willful behavior. But more than that, you will want to hear that they have successfully addressed this issue with other children, and what their strategy was.
In the meantime, you probably want to do some work at home to give your daughter better strategies for dealing with anxiety. These might include role playing interactions with other children and teachers. Play school with her, for instance, and have her be the teacher and you be the child who doesn't talk, but ham it up and make it silly so she giggles (which lets off some of the tension around not talking in school.) Or let her try on other personas, where she uses different voices and takes on superhero or other characters-- she might feel more comfortable if she’s being someone else. Introduce social situations where you stay very involved to ease her anxiety and help her to interact. I would also recommend teaching her EFT (Emotional freedom technique), which works very effectively to reduce anxiety using acupressure points - here's a link on using EFT with kids -
You will probably also want to educate yourself about Selective Mutism. SelectiveMutism.org is a good place to begin, and you may even find a good lead for an experienced child psychologist in your area. If properly treated (i.e., with techniques to manage anxiety rather than with pressure to speak), kids are able to overcome even full-blown selective mutism, but it is important to intervene as early as possible, before the habit solidifies.
Blessings to you and your daughter.
Please stay in touch and let me know what happens.