Sick goldfish... new to aquariums... am I ok?

I've had this tank for about 4 months. I have a PH kit and I keep
the water pretty near neutral. About a week ago the water started
getting REALLY cloudy. I changed the filter, and vacuumed the gravel
thinking maybe the filter would clear it up some. I get home today
and my algae eater's dead... also, I noticed that my largest goldfish
(about 4") had red spots around his fins, and the fins themselves were
verry red. The water's even more cloudy.

So I took my fish out (all goldfish varieties now) and did a complete
water change, washed the gravel, and cleaned the filter box real good.
Put new water back in, adjusted the PH, added some chlorine remover
and ammonia remover (picked both up today, wasn't using before) and
added the fish back. They seem to be moving around more now, and the
redness on the larger fish has subsided some. I'm still scared I
might lose more fish though and want to know if there's anything else
I can do. I did add about 1/4 tsp of salt to the filter box, but I'm
not sure if I should add more as the water around here is already
pretty hard. Any suggestions? It's a 10 gallon tank. I did add some
tetra's about 2 weeks ago but they all died (I found out later that
they like warmer water, but the lady at the store said they'd be
fine). It was right after they died that the water started getting
cloudy. I remove 4 of the 5 but couldn't find the 5th. Figured maybe
the larger GF ate him. Any suggestions? Should I just wait it out
now? I don't want to put them through anymore stress than I have with
the water change. I tried to get the temerature close, but I don't
have a thermometer and I think the water's a little colder now than it
used to be. Thank you to anyone who can give me some advice here.