Generally speaking anti-ulcer medications like omeprazole and sucralfate are permitted in equine competitions.
However, the emergence of injectable omeprazole has created a bit of a grey area. Generally any medications that are injectable may not be permitted to be administered unless approved by vets.
Who's in charge of the banned substance list?
Most (but not all) global equestrian bodies take their lead from the FEI Prohibited Substances and Clean Sport.
As at July 2018 neither sucralfate or omeprazole was on the FEI Prohibited Substances Database
What about racing?
Obviously it is the trainer’s responsibility to check for current standards. They change from code to code and region to region.
For example Racing Victoria in Australia stat that that ‘Oral Omeprazole may be administered up to but not including the day of a race’