No carb diet and two meals a day...sugar spiking

The Metformin could be why you are feeling sick - I was in a dreadful state taking just one tablet a day so I am obviously super sensitive.
Are you eating fats as part of your low carb diet?
Are you eating enough?
Although the accepted thinking is always low calorie and low fat, we need to have adequate amounts of protein and fat - and then whatever carbs we can cope with. I would have a stirfry with peppers, courgettes, maybe aubergine or mushrooms with one meal, perhaps a large salad or steamed mixed veges with an oily dressing or mayonnaise as appropriate. Being able to cope happily with 40 to 50 gm of carbs a day is not unusual, but the essential nutrition has to be added in for it to work. In your case injected insulin is a required element, but the fundamental principles should hold.
In the absence of fats to burn you could be breaking down the proteins which is why your BG levels are going up.
I can't advise at all on the insulin side, but I started eating low carb back in the 1970s and later on I found Dr Atkins New Diet Revolution, the 2003 edition. When he advised using a no carb diet for a few days to start weightloss it was in the form of a 'fat fast' rather than a protein party. If you can find a copy of the book it might help to read his ideas on diet and metabolism, even though it is not at all aimed at type ones.

maybe you have some kind of inflammation or infection, and/or maybe because your blood glucose, in general, has been too high ... what are you HbA1c lately?

the problem with low carb or non-carb diet is that the fat-loss comes only when ones insulin levels are not high but rather low, and that can be a bit dangerous if you get too little insulin ( and blood glucose then gets too high for fat loss as well, the body doesn´t work well when blood glucose is high and then the body sometimes changes ones muscle-tissue into blood glucose. )

I think a type 1 diabetic even with insulin resistance, need to walk on a very narrow line... and also neither get too little or too much insulin...

being a type 1 ones blood glucose raises even when eating no-carbs. Everyone also non-diabetics do produce some blood glucose themselves from transforming proteins into blood glucose.. the one kind of nutrient that the body has a hard time to transform is fat...

maybe your body/liver is very clever at transforming proteins into blood glucose.. so that you also have to have a sharp eye on your daily level of proteins.. ? just a suggestion.. do you eat enough proteins and fats so that your body does not need to also transform muscle and protein into blood glucose?

daily needed amounts of protein is around 0.8 gram pro kg bodyweight.. so a person of 80 kg would need 80 grams of protein daily to get enough, 1 egg is only around 7 grams of protein, so to keep your body from eating itself (muscles and heart) you would maybe need to eat 10 eggs daily to get enough , which is a bit boring , fish meat and other meats are also great resources of good proteins for the human body...

Are you still taking insulin with your meals? I low carb and still need insulin for meals. Even low carb meals will have some carbs in.