Checking normality without raw data Is there any way to check normality assumption only based on mean, SD and sample size? We don't have raw data.

NO
Consider that $X\sim N(1, 1)$ and $Y\sim \exp(1)$ have the same mean and standard deviation, and it becomes easy to see that you need more than those values. Sample size does not help, and it sounds like you might have a common misconception about the central limit theorem if you suspect that it would.
