Can you buy something like carafate over the counter without a prescription?

There is nothing similar to carafate available over the counter (OTC).
Carafate is an anti-ulcer medication that works by forming a complex that covers the ulcer site, which protects it from acid, so that it can heal.

For more information on Carafate see:
https://www.drugs.com/carafate.html

There are other products available over the counter that can be used to reduce stomach acid for heartburn, gastritis etc. including H2 antagonists,
proton pump inhibitors and antacids.

For more information on these see:
https://www.drugs.com/drug-class/proton-pump-inhibitors.html
https://www.drugs.com/drug-class/h2-antagonists.html
https://www.drugs.com/drug-class/antacids.html