have you ever noticed this betta biting his own tail? sometimes male bettas get into this bad habit. the reason i wonder is because the rot is primarily on the tail fin.
from what i can see on the photos, a med is not necessary. your 50% changes per day might not be enough to keep away the bacteria that causes the fin rot. i would go for 100% if it doesn't stress lil mr betta too much. as well, you mention a new filter, so large volume water changes are necessary to keep ammonia and nitrite levels at zero as the good bacteria gets established in the new filter media.
the red dots on the fin are a concern, and this is the bacteria working away at the fin. new fin growth should show up either white (on a coloured betta) or translucent on a white betta.
if this was my fish i would remove the substrate to make keeping the tank clean an easier task, as waste can be trapped between the rocks. most of my betta tanks were bare bottom all the time, and i just used plants with weighted bases or suction cups to keep them in place and upright.
from what i can see on the photos, a med is not necessary. your 50% changes per day might not be enough to keep away the bacteria that causes the fin rot. i would go for 100% if it doesn't stress lil mr betta too much. as well, you mention a new filter, so large volume water changes are necessary to keep ammonia and nitrite levels at zero as the good bacteria gets established in the new filter media.
the red dots on the fin are a concern, and this is the bacteria working away at the fin. new fin growth should show up either white (on a coloured betta) or translucent on a white betta.
if this was my fish i would remove the substrate to make keeping the tank clean an easier task, as waste can be trapped between the rocks. most of my betta tanks were bare bottom all the time, and i just used plants with weighted bases or suction cups to keep them in place and upright.