Thanks everyone for their help. I contacted a local veterarian who actually knew something about fish!

Apparently he enlists the help of an aquatist when he needs more detailed information.
Anyway, he said that the capillaries in the fins of my fish are just enlarged due to some type of stress (undetermined since I only spoke to him on the phone vs. bring the fish in), but suspects the nitrite and ammonia spikes from the cycling of the tank. He and the aquatist recommended that I do not do any further water changes since this slows down the cycling of the tank. He said let the natural biological filter to occur (3-4 weeks in my case) and then start the gradual water changes.
The vet and aquatist did not believe my fish was suffering from Aeromonas since the fish did not have ulceration and was not showing signs of lethargy. They said to continue to monitor the water and chart the progress.
As for the fantail, I decide to put him into another tank until his current residence has finished its cycling rather than risk losing him during the process.
Keeping my fingers crossed!