The following QQ plot looks with too many points out of the line, the density plot looks normal and the Shapiro Test p-value < 2.2e-16, so this is not a normal distribution but I've read not to trust Shapiro Test when I have about 1000 data points so I should conclude that this distribution is normal?
First, the density plot does not really look normal. It's symmetric, but the shape is wrong. I suggest generating a normal distribution with the same mean and variance as yours and then overlaying that density on the one you've got. I am fairly sure you will see a mismatch.
Second, a quantile normal plot is often a better clue to nonnormality.
Third, and probably most importantly, why are you concerned about the normality of this variable? What are you going to do with the variable?