Welcome to the forum
It's early days if you've just been diagnosed and it will take a some time to get your insulin doses right to control your blood glucose levels. The reason why you feel better with higher bg levels is because body has adapted to them, when you start to lower your bg you can experience what they call
false hypo's whereby you feel the symptoms of hypoglycaemia even though your levels are normal, in time these symptoms do disappear so don't worry.
Just keep reporting back to your diabetes team with your bg levels and they will advise you on adjusting the doses, once you've been diagnosed for 6 months you can go on a carb counting course such as DAFNE (Google) which teaches you the basics of carb counting and matching your insulin accordingly. There's an on-line version of DAFNE which by all accounts is very good but the website is unavailable at the moment, however if you Google
BDEC Diabetes Learning Programme later you should be able to access it.
For a good book to read on type 1 diabetes management I would recommend
Think Like a Pancreas by Gary Scheiner, it covers all aspects of diabetes management and is a really good read.
As for exercising, have a read around Runsweet, it was for set-up for people with type 1 diabetes who enjoy sport:
http://www.runsweet.com/