Dear Thea Joubert,
Good day! Thank you for posting to Microsoft Community. We are happy to help you.
As per your description, please don’t worry, we can work together to narrow down and resolve the situation.
If Form owner set Microsoft Form setting is set to "Only people in my organization can respond" that means the forms that the user want to access follows permissions option "Only People in my organization can respond" which means the creator and participator should on the same tenant. (Login the account provided by your organization with the same @yourcompany.com)

Please make sure you are using your organization account(work/school) account to access this problematic Microsoft Form link.
Also, please try to use another browser or In -private browser and check if there is any difference.
Meanwhile, could you please confirm whether other users in your organization are having the same problem when they try to access the form in the Microsoft Forms?
In addition, when you try to create a new Form/Quiz/Survey, are you able to create them without any problem? At last, does this problem happens to only specific forms or all forms listed in "https://forms.office.com/"?
Your understanding and patience will be highly appreciated. I hope that you are keeping safe and well!
Sincerely,
Waqas Muhammad