Singularity of an oscillatory integral

Question

Given $x\in\mathbb{R}^3\setminus \{0\}$, consider the following integral: $$I(x):=\int_{\mathbb{R}^3}\frac{e^{-i|x-y|^2}}{|y|} \, dy$$ Now $I(x)$ diverges as $x$ approaches to $0$, and it seems to me that the rate of divergence is $1/|x|$. Is it this actually true? And eventually what can we say abou the limit $$\lim_{x\rightarrow 0}\,|x|I(x)$$ Thank you for any suggestions.