I have coded a tool to help record everything about your horses. I have coded it to be as flexible as possible, so it works for all breeds and all disciplines. I have collaborations with Racing Associations within Australia to provide the software to new owners of retired racehorses. I am trying to expand to the USA via Texas and to the UK this year. https://horserecords.info
I took a quick look. Did not see medication records or required tests (Coggin's etc.), but that may be different from country to country.