I would definitely want to know the cause of my inflammation. There are more than the three types you mentioned. Carditis encompasses pericarditis, myocarditis, and endocarditis. All can be serious if you don't get proper treatment and rest. There are complications for each one.
It's best to be seen by a cardiologist as well and to be tested to determine the exact diagnosis. Tests may include ESR, echocardiogram, EKG, CBC with differential to start.
European Cardiologists are the only ones who have a protocol for diagnosing and treating carditis. You can do a search on the web and read about it.
Also look for COPE. This protocol was adapted from the European Cardiologists. It involves using Colchicine long term. It works too, esp. for recurring pericardits. It sounds like that's what you have. It's common after heart surgery, but you can get it by viruses and bacteria. (I'm not a doctor.) Colchicine is normally used for gout. However, it works to prevent recurrences of pericarditis.
From what I've read, I can see there is a higher chance of pericarditis recurring if the treatment is inadequate for the disease. I've read several cases online where patients were allowed to continue with the regular routine after their symptoms subsided. Usually for most people that is two weeks. And then the symptoms recur be the heart isn't healed.
I have pericarditis, mild myocarditis plus complications. The treatment I received so far has been: 1 month bed rest; meaning no exertion such as exercise, lifting, and basically staying in bed or a chair. 1 month of NSAIDs in high doses. 1 month of Colchicine in high doses. And pain killers as necessary. For the next 3 months I will continue on half the NSAIDs dose and half the Colchicine dose. I take Nexium to prevent problems with the NSAIDs. I am now able to go for slow walks and can increase intensity and distance as tolerated. However, I've been restricted from cycling and resistance training, two exercises I love doing. I am on other medications as well for the complications.
My doctors, 2 primaries and 1 cardiologist, put me on the Colchicine right from the beginning. Usually Colchicine isn't used until the pericarditis returns.
Yes, I would want to know the cause of the inflammation and deal with it accordingly.
Have you spoken with your surgeon about this? I would deal with them before the GP, just to be on the safe side. I can see why you would not want to continue anti-inflammatories indefinitely.