I have this frequently also (palpitations) and they often induce insomnia. FWIW my perspective is this:
A few years ago I overtrained (I'm a keen martial artist) on the back of years of playing Australian rules football and periods of extreme overwork. The upshot is I damaged my sympathetic nervous system and this is where likely your problem lies.
I had a lot of expensive treatment, including a cardiologist (for the palpitations and elevated HR), and ironically the free NHS treatment at the Royal Free Fatigue Clinic was the most effective, and involved no taking of drugs, but a bit of education and simple graded exercise therapy - that and a LOT of determination on my part to sort things out.
Basically your various systems, endocrine, sympathetic and parasympathetic nervous, digestive, immune, are all interplay with each other and your mind. An example; which comes first, the thought or the feeling? Very often sensations in our body are misinterpreted, e.g. hunger and depression. The sensation of anxiety comes from the hormone cortisol and the reason it is in your system can be for a variety of reasons.
In my case, because of my experience of overtraining, my body has 'learnt' to release too much cortisol when I exercise. Ironically, it's doing MORE exercise that controls it, but in a very carefully managed way. Essentially what happens is, if I allow my HR to be too high for too long, it overstimulates my SNS (sympathetic nervous system), kind of like hiccoughs, meaning I have an elevated resting HR, palpitations, diahorrea, head aches, fatigue, and of course - insomnia.
Now however, it is not just exercise that induce symptoms, it can be other things as well - general stress and overstimulation, certain foods, and esp alcohol (goddammit). Cortisol is released due to any sort of inflammation in your system, such as illness, allergies, infection, or injury. Another contributing factor that can lead to these problems is childhood trauma. No one knows exactly why this is, but the assumption is that it has something to do with the bodies adaption mechanism maladapting to certain stimuli.
For professional help, my advice would be to look toward Chronic Fatigue specialists. Graded Exercise therapy is really really effective, but it takes a lot of discipline. It's not just about that, it's also about really carefully constructed routines.
The most important thing I have done to help manage my problems was diet. It should absolutely be the very first thing you examine and experiment with, perhaps you could include a food diary (I had to do this) as well as a sleep diet. Everything else is pretty much downstream from what you eat. At the risk of sounding like I am promoting a fad diet, my suggestion is to look at the paleo approach.
The paleo approach has two distinct areas, but the principle is the same. There is the basic approach and the auto-immune approach (which you won't need to concern yourself with). The idea behind the paleo approach is that modern eating habits are out of step with the eating habits we evolved with, and what are bodies tolerate or need varies from person to person. If you eat too much of certain foods it can induce an inflammatory response, which in turn produces cortisol, which over time has the health implications exactly like the ones you have outlined.
For me, this means almost no sugar at all, not even fruit, extremely high fat, oils and protein, and very low carbohydrates. So typically I eat lots and lots of nuts, avocados, Low GI vegetables, meats and lots of olive oil and animal fats. But it also means the quality of the food has to be very high. I also try to eat lots of pro-biotic sauerkraut to make sure have good gut flora. The difference has been that I don't gain weight even when I eat a lot, but the main difference has been to my mood. I used to be really up and down, but now I am much more stable. Alone, the diet won't STOP me from getting symptoms, but it makes it much easier to manage when I induce them through other means.
I hope this gives you enough to be starting with. I know how difficult it is and how little GPs know and understand about this. I dived deep down the rabbit hole on this. I also can't guarantee that once you have handle on it you won't still have problems with it from time to time, but having a set of tools to tackle it with is very empowering.