Photoshop Elements can do some pretty strange things sometimes.
Sometimes a Tool from the Toolbox will not act the way it should. When that happens the first thing to try is to go up in the Options bar and way over on the left side there's a tiny arrow you can click on and choose Reset Tool.
In this case, since your Blur tool is missing you should check something else first. The Blur tool shares the Toolbox with two other Tools. The Smudge and Sharpen Tools.
You can tell if a Tool shares a space if there's a tiny arrow next to it. Just click and hold with your mouse on the Tool to see the other Tools. Then just move your mouse over the Tool you want and release.
Add a comment to this page and let us know if that solved your problem.
Good luck! Rick
BLUR TOOL by: Veree
Thank you Rick that was exactly what I needed to do, I would never have known if you hadn't helped me know that the space shares 3 tools.
Your Welcome! by: Rick
Excellent Veree! I'm glad that solved your problem. And thanks again for submitting your question. I'm sure other visitors have run into the same situation and will benefit from your asking.