Should other factors also drive final model selection?

I have used a linear mixed effects model to identify factors associated with depression scores over time (measured at 3 time points). I have been advised to use the AIC/BIC to assist with model selection. I used a forward selection approach (although you could say it is more bidirectional elimination, as I added and removed variables depending on significance and the AIC/BIC).

I ended up with two models. The final model (I will call this Model A) which only included factors significant at p

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