While treating you can warm the tank up another degree C, maybe two. Be careful with Melafix. I'd cut the dose in half for a Betta.
While you're treating him for fin issues, I'd change half the water twice a week. Vacuum the substrate and otherwise keep the tank very clean. Add Seachem Prime (water conditioner) to the tank @2-drops/gal daily.
When his finrot problem gets better, you can cycle his tank. This provides the best water quality for your fish -- crucial for fin problems. Not as important, it makes less work for you.
CYCLING: the two-sentence tutorial
Don't worry about pH. But you will want to get one of these: Amazon.com: API Freshwater Master Test Kit: Pet Supplies
So you can keep an eye on water quality, and so you can cycle your tank.
High-quality food is necessary for fin recovery. (Unfortunately, Hikari is not the best.) New Life Spectrum Betta or small fish formula is recommended. Also good is Omega One Betta Buffet. You can knock off the FD bloodworms.
Welcome to the forum.