It is good to know the difference between bad fats and good fats. Bad fats, such as those that are animal based, can cause you to have higher cholesterol levels and develop heart disease. Good fats are from vegetables, fish or nuts, and while they are still high in calories, they have many properties which can lower cholesterol and improve heart health.
If you suffer from fibromyalgia you should cut unhealthy fats from your diet because these are bad for your heart and can actually increase pain sensitivity and inflammation.
So, try to avoid red meats and full-fat dairy products, and try to incorporate healthy fats into your diet like olive oil or coconut oil. Both olive oil and coconut oil have shown to have anti-inflammatory properties and can help reduce joint inflammation., 
There is also evidence to support the view that omega-3 fatty acids (found in fish like salmon, tuna, and mackerel) can also reduce joint inflammation.