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Using anti-biotics to treat fin rot is not the best way to go about it.
The white stuff on the tail is excess mucous produced by the fish to cover the damaged tissue.
Epsom salts (magnesium sulphate) does not treat fin rot. It is used to draw fluid out of fish.
Rock salt, swimming pool salt, aquarium salt (is sodium chloride) and this can be used to treat fin rot. See below for instructions on salt.
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The fact this continues to happen would suggest there is something in the tank that is catching and ripping the fins. It is either the driftwood, plastic pots, plastic plants or gravel.
I would remove the pots and driftwood and see if it helps. If it still happens then remove the plastic plants.
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Make sure you have live plants in the tank for the goldfish to eat. They need a lot of plant matter in their diet to maintain a healthy immune system. If they don't get enough plant matter in their diet, they can be more prone to infections and minor wounds can take longer to heal.
Duckweed is a small floating plant that most goldfish love to eat. You can grow it outdoors in ponds or in aquariums. Just add some to the tank each week and let the fish help themselves to it.
Other plants that are good for them include Ambulia, Hygrophila polysperma and narrow Vallis.
You can give them small amounts of spinach, pumpkin, zucchini and some other fruits and veges. Just make sure they are free of chemicals and rinse them well before putting in the tank. You can put the veges in boiling water for a minute to soften them up and the fish might prefer that over fresh.
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SALT
You can add rock salt (often sold as aquarium salt) or swimming pool salt to the aquarium at the dose rate of 1 heaped tablespoon per 20 litres of water. If there is no improvement after 48 hours you can double that dose rate so there is 2 heaped tablespoons of salt per 20 litres.
If you only have livebearers (guppies, platies, swordtails, mollies), goldfish or rainbowfish in the tank you can double that dose rate, so you would add 2 heaped tablespoons per 20 litres and if there is no improvement after 48 hours, then increase it so there is a total of 4 heaped tablespoons of salt per 20 litres.
Keep the salt level like this for at least 2 weeks but no longer than 4 weeks otherwise kidney damage can occur. Kidney damage is more likely to occur in fish from soft water (tetras, Corydoras, angelfish, Bettas & gouramis, loaches) that are exposed to high levels of salt for an extended period of time, and is not an issue with livebearers, rainbowfish or other salt tolerant species.
The salt will not affect the beneficial filter bacteria but the higher dose rate (4 heaped tablespoons per 20 litres) will affect some plants and some snails. The lower dose rate (1-2 heaped tablespoons per 20 litres) will not affect fish, plants, shrimp or snails.
After you use salt and the fish have recovered, you do a 10% water change each day for a week using only fresh water that has been dechlorinated. Then do a 20% water change each day for a week. Then you can do bigger water changes after that. This dilutes the salt out of the tank slowly so it doesn't harm the fish.
If you do water changes while using salt, you need to treat the new water with salt before adding it to the tank. This will keep the salt level stable in the tank and minimise stress on the fish.
When you first add salt, add the salt to a small bucket of tank water and dissolve the salt. then slowly pour the salt water into the tank near the filter outlet. Add the salt over a couple of minutes.
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