Well I'm not sure it's quite so formulaic as that - even on mixed insulin, everyone's needs will be different. But I agree that is a diet based mainly around carb-containing foods, from the sounds of it. On mixed insulin you will need some carbs to "feed the insulin" (this is one reason why a lot of us don't like mixed insulin - you have to eat to match the insulin rather than taking insulin to match what you feel like eating) but you may find that eating a bit less carbs may help you feel better, if the carbs are sending you high and leading to you feeling tired. On the other hand it does sound like you have some other issues going on at the same time, so definitely worth seeing a doctor about and not just assuming it's all down to diabetes.
There are really 4 keys to managing insulin so that you feel as well as possible as often as possible. The first is testing often to see where you are. Especially when you're feeling particularly unwell. This will help you to know, first off, whether it actually is high or fluctuating blood sugars that are making you feel that way (because it may not be!) It also helps you to judge how effective your insulin and diet choices are, so you can know what you have to modify.
The second is feeling at ease adjusting your own insulin dose. On mixed insulin, this can get a bit complicated because you're always injecting for this meal AND for the rest of the day, all at the same time. So you can't, say, take more insulin because you want a big breakfast, without getting into trouble later in the day because now you have too much insulin for the rest of the day! So everything has to be done in moderation. But whether you are on mixed insulin, or a basal-bolus regime, it's impossible to achieve your best results if you have to wait on a doctor or nurse to authorize each dose change. Getting comfortable adjusting your insulin, if you're not there yet, is a process, and should ideally be taken on with the help of your doctor, or at least with your doctor being under advisement that you intend to learn how to do it (personally, I figured it out on my own at home - it's not something that is so unthinkably complicated that you must have professional help to do it, but it's generally best to have some guidance when you're getting started!)
The third is knowing how to carb count. It's again, not very complicated or mysterious, just a matter of knowing how to look up information about the carb content of your foods and apply it to what you're eating. This will give you an idea of how many carbs your eating and whether and where you might need to reduce carbs in your diet to help make the insulin you take be more effective, and reduce the number of high blood sugars you have so that you feel at your best more often! The idea is to have a diet that is low to moderate in carbs and higher in protein and vegetables, so you're still getting good nutrition and feeling full but with fewer carbs (which are the things that push blood sugars up and generally require us to take more, rather than less, insulin).
And the fourth one, is doing just that - reducing carbs to a level that is on the one hand something you can live with in your daily life (no sense being so restrictive that you're miserable) and on the other hand is a level that doesn't give you lots of high blood sugars that your insulin can't keep a handle on. Now you want to go at reducing carbs slowly and gradually, because if you reduce carbs too much without also reducing your insulin then your blood sugars really might go too low. So if you go slowly, then you can reduce both carbs and insulin, stepwise, using your testing (key #1!) to help you know when it's time to adjust your insulin downwards (key #2 - see how it's all interconnected?) For some people, when carbs in the diet are low enough ("low enough" being a different amount for each person!) they end up needing so little insulin that they can come off it.