OP, I had an IQ test when I was 7 (never fully understood why! Something to do with my parents long custody battle and my ability to understand I think). It put me somewhere around the middle (slightly over on one subtest, slightly under on another) and until that point my mum and teachers thought I was smart, and I believed I was too. I'm fairly sure the results influenced the way mum viewed me after that, though she never let on in so many words (but in retrospect I think a child can pick up when a parent believes they have limits) and I ended up with middle of the road GCSEs and pretty rubbish A levels.
As an adult I was sure my test results didn't accurately reflect my intellectual potential. I had this inner belief I was smarter than people believed and my results indicated. I had a lot of trauma in my life, so admittedly this did also impact my A levels.
Anyway, I made the decision for a re-test. I came out with an IQ over 135 on the WAIS-IV, which is very high. I then had the confidence to take the MENSA tests, and they placed me with an IQ of 155 and I joined MENSA (I've now left as it was more about proving something to myself than actually gaining anything from the membership!! And it cost a fortune!!)
I subsequently had the confidence to complete a degree, MSc and PhD.
I know the theory is that IQ can't change - but I believe it can. I also think when you test kids there are so many variables which could make their score seem lower. The main factor to success is hard work and self belief. I firmly believe that.
All that said, having some randomly high score on an IQ test, or getting good grades at school are IMO not that important. One of my children is very sporty. I encourage that and I expect he'll go into the forces, or do something with his sports in the future (maybe coaching, teaching, sport science or something). The other one has a flare for art and music and I expect it may become the route he takes.
Academics are overrated. Encouraging your children to do what they love, and work at it, is most important.
I overcompensated by getting all my degrees as I had a point to prove to myself, and also to my mum. However, i am really not interested in academics. My dream would be to have a little coffee or tea shop by a lake somewhere. My mum could have noticed better my strengths as kid and encouraged me to pursue what I was naturally into. Instead I'm now stuck in a job which, I guess I like, it earns well, but it's not my passion. I don't love it.
It's far better as an adult to be happy doing a job you love, than be a miserable lawyer or financier etc... IMO