Your code is blindly rotating the transform. That approach won’t trivially work with clamping.
Instead you need to track the angle of up / down and clamp it.
Here’s one example, there are THOUSANDS more available in tutorial and raw code format:
http://wiki.unity3d.com/index.php/SmoothMouseLook
When you do so, keep this in mind:
Notes on clamping camera rotation and NOT using .eulerAngles because of gimbal lock: