Why can a tremolo make a rattling sound? I changed the strings to thicker ones. I thought that the problem was a raised tremolo (but it didn’t visually look like it), tried to tighten the screws on it and it didn’t help. What else can I check myself or is it better go to a specialist?
Take the bar off - does it stop?
Most common cause is the actual whammy bar rattling in its thread.
Fix is a few turns of PTFE tape on the thread before you screw it in, available from any hardware/plumbing store. Don't use sticky tape of any kind. PTFE is "teflon" & won't stick or jam.
If that's not it, you're going to have to give us better information.