Eunice here from Shopify, thanks for posting, and welcome to the Shopify Community. I'm sorry to hear you're having trouble with your checkout, that's something we definitely want to look into as soon as possible!
While we’re not able to provide account-specific support via the Community at this time, you can visit the help center to log in to your account and create a support request. From here you can choose from the options to live chat, schedule a phone call, or email with a support advisor.
Before you contact Shopify Support there are a couple of things you can troubleshoot now:
1. Are you able to replicate the issue by placing a test order on more than one device? If you're not able to replicate the issue yourself, and you can check out without any issues, then I recommend asking the customers who have reported checkout issues to clear their browser's cache and cookies and try again.
2. The next thing you can check is your theme. Please add a Shopify free theme to your theme library and then preview the theme. In the checkout area are you able to replicate the issue? If the checkout is working fine on a new theme then this could indicate an issue with the live theme you are currently using.
Please note, these are troubleshooting steps only, please contact Shopify Support for account-specific support.
I hope the above points you in the right direction and that your checkout is back up and running soon!