Possible Betta fin rot

[BettaFishGirl]

I rescued a Betta at PetSmart a few months back and she has been doing amazing and super energetic and happy. Her name is Beth. I tried to put a few ghost shrimp and snails in her tank, within an hour she killed all of them, so she clearly doesn't want any living being in her tank other than her. It is a 3 gallon planted tank and had been running for 2 months. I didn't cycle it beforehand but I used mature filter media from my other tanks when I set it up, so I put her in right away with the mature media. It is heated at 78 degrees.
Water parameters:
Ammonia-0
Nitrite-0
Nitrate-5

Over the past couple weeks I've noticed her fins have started to get jagged and almost rot away. I thought it was fin rot but there is nothing sharp in the tank and the water parameters are perfect, so now I think maybe she's nipping her own fins? She is extremely territorial and she does this thing where she will go side to side really quickly when I'm in front of her and kind of get her fins in her face so maybe she just nips at them? I've never seen her do it but she only pays attention to me when I'm in the room so she probably gets distracted. There is no other fish, shrimp, or snail in there besides Beth.

It also looks like she has ick in her fins but when her fins were full there was a white outline so it just the little white outline left, not ick.

The only type of medicine I have is aquarium salt, should I add that? Any help is appreciated. Thank you so much! Pics attached

 

[Obsessed with fish]

Looks like fin rot to me, your paramaters look fine so it could be due to a bacterial infection. Do a 75% water change, clean the gravel and scrub the glass to get rid of the infection. After you do the water change put some aquarium salts into your water, one level tablespoon per 5 gallons of water.