You should be testing your bromine level. It doesn't sound like it's enough given your weekly dose so when there is no bromine and you only have copper ions in the water, the water is not disinfected at all against fecal bacteria or transmission of viruses. See
this post for more technical info. Copper is primarily an algaecide, not a disinfectant, and if you are not careful with the copper level or if the pH gets too high, you can stain pool surfaces and turn blond hair greenish. That's why we don't recommend it.
As for bromine, it is more expensive and can get used up more in sunlight than chlorine (with CYA). Is your pool exposed to sunlight all day?
The problems you mention at your friends' pools are likely from them not properly managing those pools. People here on this forum who manage their pools according to the Pool School also report virtually no smell (in my pool, I have to churn the water near the surface to get the faintest detection of a clean bleach-like smell; others don't smell anything). Red eye comes either from improper pH or if one is in the water with eyes open for a while, then it's primarily from the salt level since human tears have 9000 ppm. Saltwater pools tend to be easier on the eyes with their 3000 ppm. Red eyes don't come from chlorine unless the level is very high (usually without CYA in the water) or, more likely, there is a buildup of chloramines.
The active chlorine level that is the minimum to prevent algae growth is the equivalent of only 0.07 ppm FC with no CYA so is much, much lower than found in some commercial/public pools, especially indoor pools and it's lower than in bromine pools. This very low active chlorine minimizes the amount of volatile and irritating nitrogen trichloride while the regular dosing and maintaining of the chlorine level prevents any buildup of other chloramines (monochloramine, dichloramine, organic chloramines) while preventing algae growth and killing pathogens quickly.
If you've been dosing with sodium bromide for a while (2.8 ppm * 4 = 11.2 ppm bromide), it may be too late for you to even try out the chlorine method in your pool. Once a bromine pool, always a bromine pool, or at least you're stuck with a bromine pool for quite some time. The reason is that when bromine gets used/consumed, most of it becomes bromide again. A small amount of bromine outgasses and some is removed in the filter as combined bromine on organic debris, but you pretty much have to do a substantial drain/refill to get rid of it. It's more or less a one-way commitment. I'm not sure why you are adding sodium bromide weekly. You normally establish a bromide bank large enough to produce a bromine level quickly enough from an added oxidizer and then just add a very small amount to maintain that bromide bank. See
Using Bromine in a Spa (or Pool) for more info.
Neither chlorine nor bromine will last a week in sunlight unless one doses to much higher levels and uses CYA in the water. That's why it's more common to see Trichlor tabs for chlorine and bromine tabs (BCDMH or DBDMH) for bromine since they are both slow-release, though have other problems with what they also add (CYA for chlorine and DMH for bromine). That's why you'll see most people on this forum initially establish a CYA level and then dose their pools regularly (usually every day or two; with a mostly opaque pool cover, twice a week) with bleach or chlorinating liquid or have an automated dosing system such as a saltwater chlorine generator or a peristaltic pump or The Liquidator.
To be designated as a swimming pool disinfectant, a product must go through
EPA DSS/TSS-12 efficacy testing and also be demonstrated to be safe. There are only three chemicals that have been approved (technically, it's products that are approved, with specific concentration instructions, but all products have one of these chemicals) and for pools these are chlorine, bromine and Baquacil/biguanide/PHMB. For spas, Nature2 with MPS (monopersulfate) has also been approved, but only for hot water temperatures (i.e. not for pools). Though you are using bromine, you are not doing so in the prescribed fashion where the bromine level is never below 2 ppm (or 0.8 ppm when using copper/silver or copper only ionization as with
these products that are certified to NSF Standard 50).
It is more usual for a residential swimming pool to develop algae than for people to get sick or ill effects, but it is not unheard of and we recently saw a case in
this thread of
Pseudomonas Aeruginosa that is more commonly seen in improperly treated hot tubs. On another forum, there were quite a few incidents of not only hot tub itch/rash, but also hot tub lung and one case of Legionnaire's Disease where the person nearly died. Some of these hot tubs used "alternative" methods of disinfection not approved by the EPA; others used chlorine or bromine but in insufficient amounts so their levels were too low or zero; still others had a longer term buildup of CYA making the chlorine less effective.