I received a cease-and-desist letter saying that my website tracking prices of certain…

Web scraping is a grey area, with various different potential legal theories under which a plaintiff may take you to court. In the case of the United States, the main ones are copyright infringement, violation of the Computer Fraud and Abuse Act (hacking), and trespass to chattels.

Given that Amazon is aware of your activities, it is likely that they have initiated measures to detect and block your crawlers, or feed them false data. Further, regardless of whether your activities may ultimately be within the bounds of the law, ignoring this order may result in costly legal proceedings being initiated against you. It's highly likely that continuing to run your website is a bad idea.

If you believe Amazon is too draconian in its interpretation of the law, you may consult with the Electronic Frontier Foundation, a digital rights non-profit which may issue amicus curiae briefs on your behalf or provide funding for legal counsel given that they find there is grounds to defend your activities.