No, if you have tested positive for COVID-19 on or after Oct. 21, 2020 (e.g., within 90 days of start of classes on Jan. 19, 2021), you do NOT need to be tested again or self-quarantine before the start of classes in January. Per CDC testing guidelines, anyone who has tested positive should not be tested again within 90 days.
You must provide proof of your positive test result to the Protect Purdue Health Center by emailing quarantine@121.health.