Brake shims are meant to minimize the noise that is produced when you apply the brakes. These are essentially adhesive pads constructed out of either metal or rubber, which go between the brake pads and calipers. The shims are capable of adjusting to any special discrepancies here, and make sure little to no noise is produced. The most you would hear out of the caliper-pad pair is a bit of rattling.
Attaching Brake Shims
If you hear loud squealing coming out of the braking system, it means that the brake shims are either worn out or have been dislodged. It makes sense to chalk up this noise to the rotors, but that is not where the blame lies in most scenarios. The brake shims may have gone missing when you attached new brake pads, or as a result of something else entirely. What needs to be done to prevent this is, attach the shims and pads separately. The former usually come with an attached adhesive material, so that they can be securely affixed to the back of the brake pads.
If the noises persist, it could still mean something other than the brake rotors is awry. It may be that the brake shims lack ample lubrication to reduce the friction, which is causing the sounds you are hearing. Applying the right amount of grease or another suitable lubricant should take care of that issue, helping the shims to properly align the pads with the rotors. That way, you can have all three parts functioning the way they are supposed to. In most cases, a thin film of lubricant would suffice.
Squealing noises are what most commonly signal a missing or insufficiently lubricated shim, but your brake system can exhibit other symptoms as well. One of these is bad brake response, and another is pulsation of the brake pedal. Each can be traced back to improper alignment of the brake pad with the calipers, preventing the former from properly contacting with the rotors when you press the brake pedal. Moreover, this can wear down both caliper and pads a lot faster, making it necessary to get replacements.
The alternative to that is driving around with brakes that are not 100% functional, which invites too much risk even when you mostly drive below 50. The best way forward is to get a repair mechanic to look it over, and then decide your next move based on what they recommend.