Hi,
From your description you sound as if you were in ketosis and that normally indicates type 1. If you are slightly (or even much) older than a child or adolescent it may have taken longer to develop, hence type 1.5. or LADA (latent autoimmune diabetes in adults)
What you now need to to is to work out how best to use insulin to control it. I was diagnosed in very similar circumstances. I left hospital with a similar regime, including the fixed number of carbs per day and a sliding scale of rapid insulin. The number of carbs a day was also similar. Unlike you I was given advice on adjusting my insulin.
Your basal (lantus) isthe insulin that covers the glucose released by your body, its purpose is to keep your blood glucose levels in between meals. If you didn't eat, in an ideal situation you blood glucose level would remain stable.
Your rapid (lispro) covers the meals, it starts its action fairly soon after eating, peaks at about 2 hours and then has a tail where it continues to 'work' for another couple of hours.
If your hypos occur more than 2 hours after eating, they are likely to be because of too much lantus or exercise. What you can do to test this is to divide your day into segments and test each segment at a time. Miss a meal and test your levels. They should not change by more than about 18mg/dl(1mmol). If Bg is going down more than this then you need to lower you basal. Do this by no more than 2 units at a time and leave it 3 days to see if things have improved. Overnight is probably the best time to get right first . See
http://www.diabetesdaily.com/forum/articles/16675-basal-testing-multiple-daily-injections This explains it far better than I can.
If your hypos are within 2 hours of eating, then the culprit is more likely to be the rapid insulin. I have to say this is where a fixed carb regime came in useful. If you eat the same amount of carbs at the same time of day then it is relatively easy to adjust the insulin to achieve a reasonable result. Test at 2 hours postprandialy and then adjust the following day by a unit up or down depending on readings. The targets I was given initially was to ideally have a rise of no more than 50mg/dl (2.7mmol/l) and not to go above 150mg/dl (8.3mmol). When you have sorted out how much insulin you need for your normal amount of carbs you will find it easier to be more flexible on the number of carbs you eat. There is far more about carb counting/dose adjustment on the Bournemouth (BDEC) link given by Trinkwasser.
It is important that you test regularly to understand your bodies response to food, insulin and exercise.If you can't get suffcient strips prescribed (probably an average of 6 per day to begin with) I would buy them myself if at all possible.
You won't get it right all the time. Things may( and will) change. As you've just been diagnosed it may very well happen that you have a period when your insulin requirements get lower. With classic type 1 this is often called a honeymoon, with the slower onset (LADA) there may several cycles of needing less insulin, followed by needing more (this is still happening to me 4 years after diagnosis and can be very frustrating)
Finally if you are having frequent hypos it points to too much insulin. This will make you eat to feed the insulin, you'll put on weight. However it is not unusual for people to put on weight after diagnosis since they have often lost a lot when they had undiagnosed high blood glucose levels before diagnosis.
Thats enough for now (hope its not overload!)