Salt system control units will give a reasonably accurate reading for the salt content in the pool, with one exception, when the cell has expired. You did the right thing in having the salt tested independently. Your service tech can test your salt for you and should be doing so as a matter of course every 3-4 months just to make sure the system is reading correctly and there are no other issues.

Many homeowners, when purchasing salt systems for the first time, are not informed of all the relevant information on the life of the systems. Do not presume that once you buy the system and have it installed it will operate tirelessly for the life of the pool. If we use the Hayward Aqua-Rite or Pro-Logic systems as an example, the cells used on these systems have an operating life of 10,000 hours. After that the life of the cell expires and the cell requires to be replaced in order to continue to produce chlorine. If the clients pool runs for 9 hours per day 7 days per week the cell will be required to be replaced in 3 years and 3 months.

A replacement cell for the Hayward system can cost up to $650 for another cell that will only last another 10,000 hours. Several manufacturers have developed aftermarket replacement cells that directly retrofits into the Hayward unions. They are cheaper than the Hayward AND they have a stated life of 15,000 hours, coupled with the fact that the cell itself is see through and the warranty is 3 times better than that of the Hayward, it appears to be a "no brainer", however, buyer beware, several companies that produce these aftermarket cells including Compupool have gone out of business, therefore so has any warranty

Personally, I would replace the system with the latest technology from JANDY. 
Jandy use proven technology to ensure that their units do not suffer from board failure with the slightest surge, a common complaint with the Hayward systems.

It is a common misconception that excessive Chlorine causes the burning sensation on your eyes. "Eye Burning" is usually the result of too little chlorine in the pool water or an incorrect pH balance.

Have the water tested by a professional who will be able to test and distinquish the levels of Free Available Chlorine and Total (often called Combined) Chlorine. The golden rule is that these two results ideally require to be close to each other, for example, if you have a free level of 2.3ppm and a total or combined level of 2.8ppm then you are in good shape, however, if you have that free of 2.3ppm and a combined of 3.4 then your pool is loaded with Chloramines which are a nitrogen compound and will cause eye irritation. The most common Chloramines are NHCI and NCI these Chlormaines are present from rain, perspiration and urine among other things. The way to reduce the deficit between the two readings is to superchlorinate or shock the pool, this will burn off the Chloramines and bring the combined levels down to equal the free levels which in turn will mean that your pool is full of free available chlorine ready to act as a sanitizer. Check the pH level as this can also be effected by heavy rain as it causes an inbalance in the Alkalinity which in turn allows the pH to "bounce".

The introduction of foreign matter coupled with pool filter operation may cause cloudy water (algae may also cause cloudy water). Check the filter run pressure, if it is over 10psi higher than the start-up pressure after cleaning then the filter is not operating effectively and needs to be assessed for either cleaning or element replacement.
A high pH level can also be attributed to the cause of cloudy water. Your pH should be checked and adjusted weekly as part of your general pool maintenance.
Another factor which can cause cloudy water is poor circulation or low filtration times. Some filters/pumps require to be be run continuously, such as above ground pools. Some pool owners are reluctant to do this and mistakenly blame the lack or excess of chlorine for the cloudiness.
Poor circulation occurs most frequently when the main drain is turned of and the pool is run purely on skimmer filtration. The skimmer circulates only the surface water which results in a build-up of contaminants in the deep water of the pool. Main drains should always be in operation except when using an automatic pool cleaner through its own suction outlet, if using a pool cleaner through the skimmer, the main drain must be open for suction.

Having your pool re-finished is not only a big undertaking but also a considerable financial investment. The first month of pool service is the single most important phase of any re-finish.

I would strongly recommend you contract with a certified, licensed and insured pool service company for that 1st months service. Average cost for the first month pool service following a re-finish is $385. This involves 6 daily visits per week for the complete month to monitor the pH, Chlorine and Alkalinity levels, daily sweeping and vacumming as required with a brush vacuum only, filter cleaning as and when required which could be as much as every 3 days, balancing Cyanuric acid level at week 3, maintaining checks on Calcium hardness levels throughout the month and balancing the pool for swimming during week 4.

If you value the investment in your new pool finish contract with a service professional, take on this 1st months service yourself and you risk damage to your new pool finish.