I bought illustrator but I can't use it.

try @Manan Joshi' suggestion first. it contains the most likely fix.

only if that fails, proceed to these steps - https://helpx.adobe.com/enterprise/kb/resolve-trial-and-license-expired-errors.html

if that fails, https://helpx.adobe.com/download-install/kb/adobe-license-issues-keychain-credential-mgr.html

below are solutions some users reported:

if those all fail, change your cc language. eg, try international english - https://helpx.adobe.com/creative-cloud/kb/creative-cloud-trial-mode.html

if that fails, change the install location

Hi @Riya306079584fcz,

Try the steps mentioned in the following link
https://helpx.adobe.com/hk_en/manage-account/kb/stop-creative-cloud-trial-mode-after-purchase.html

-Manan