Well, normal distribution of "data" (sample data) is irrelevant. The model assumes normal distribution

in the populations from which the sample data are drawn. Or, more simply, the prediction errors from

the model should be normally distributed. Since your sample size is very small, violation of this

assumption could be problematic (AFAIK). At the same time, one cannot demonstrate with sufficient

evidence that indeed the error distribution in the population is normal. Maybe there is some

reference which demonstrates that ANOVA is robust against non-normality even in small samples.

is it mandatory to use a 2-way repeated measure ANOVA or is there any exception condition?

You did not state a clear research question, therefore it is difficult to comment on which approach

could be useful here.

With kind regards

Karabiner