If your house is over 20 years old, it is likely to have asbestos materials in it. You need a professional asbestos removalist to test for asbestos to identify whether your house contains asbestos.
If you accidentally discover asbestos materials during work, end the work immediately. Contact a certified and professional asbestos removalist to conduct a thorough risk assessment, and perform asbestos testing work if it's needed.
Since asbestos is hazardous material, only an authorised facility is allowed to accept asbestos waste. Therefore, you should only contact the EPA in your state to locate a facility licensed to accept asbestos waste.