You should be able to access your QuickBooks Self-Employed (QBSE) account after successfully updating your billing information. Check the following article for more information: How to resubscribe to QuickBooks Self-Employed.
In case, the account is still showing as suspended, I suggest reaching out to our Product Support team. They have the tools to get into your account and further check why your QBSE account is still showing as suspended.
Here's how to reach them:
From your QBSE account, click the Help icon at the top.
Click the Contact Us button at the bottom of the page.
Provide some insight about your concern and then click the Continue button.
You can choose either to Get a callback or Message an agent.