There are two main methods to figure this out. You could try adding some diatomaceous earth or a sand filter to test it. Just a scoop or two will do it into the skimmer. Immediately after adding it look at the pool jets and returns to see if you can physically detect cloudy water coming back in. If you can, then you probably have a filter issue and will need to address it in a different way. Make sure you don't add diatomaceous earth to a cartridge filter. A little bit of cellulose fiber-based filtration powder can work if you want to see if anything comes through but diatomaceous earth can pack into the cartridge fold and cause excessive strain on fabric elements so you want to use that with caution.
Another method is to test the filter by connecting a vacuum hose and skimmer suction port. You could see if the Jets or returns show any cloudy water coming back through. Of course, you actually have to have dirt on the floor of your pool to see if this method works.
The first method assumes you have a pressure base sweep that uses unfiltered water and if you have a backwash valve it's possible that the valve seal or diverter could be failing, which will allow dirty water to bypass the filter and recirculated back into the pool. However, it's more common for the filter to have an internal problem then a failed valve.
If the pool filter shows dirt coming back through it's important to clean the filter and backwash valve thoroughly. The filter cleaning should be a full disassembly and inspection of each internal part, which is something a professional pool service company can do for you. If you have a sand filter blowing dirt back into the pool, check to see if the sand is more than 3 to 4 inches old. If so, it could be ready for a sand change. Over time, water going through these particles tends to round them out and lose their sharp edges making the sand like small marbles.
Replacing the sand typically cost several hundred dollars and can put you at about 50% of the cost of a new filter. If your residential pool owner you may not need your filter running 24 hours a day and a cartridge filler can do the same job in half the time. There are different filters for different needs so it's important to talk to your pool specialist about the needs of your pool and the filter requirements.