Rattling noise under 02 Corolla

It is hard to say from your description, but it might be the exhaust manifold shield has some bolts missing or have come loose. I have an early 90’s Corolla and had that problem at one time. For me I just needed to re-tighten the bolts that hold it on. In my case it was most noticeable at idle.

The other thing you may be seeing in that area you mention is the engine splash shield. On my Corolla at least, that part is made of plastic, not metal. But you might think it is metal if you didn’t examine carefully. Again, that part is bolted to the car and the bolts can come loose and could make a noise.

The source of sounds coming from a car is often hard to determine. A mechanic has a tool called a mechanic’s stethoscope which can narrow down the area that a sound is coming from, making it easier to diagnose.