Could my betta be sick?

[beta queen]

I am new to the betta world since my son moved home and brought Jaeger with him. I am so attatched I can't believe it. I'm wondering though if I might have a problem, I was looking on this website and came across Myates who has a picture of one of his bettas I think. Jeager looks the same as his red betta, but he has what looks like clear balls on the tips of his fins. I thought all their fins and tails were suppose to be smooth and solid not stringy looking. I went to the store and bought some Melafix but could they help with how much to add alittle better than 1 tsp for 10 gallons? Thanx to any help anyone can give me.