Hi Maureen and Welcome!
Insulin can be a great tool to help manage Type 2 Diabetes (I also use Levemir at 10u each night) but it does sound as if this one type of insulin may not be working out best for you.
...the sugar levels are not controlled properly yet, and often the site of the injection comes up like an angry mosquito bite and irritates for days.
I am not a Doctor but it seems you are reacting (or even allergic) to the injection... not necessarily to the "insulin" itself but to the additives used either to help preserve the solution or to delay it's absorption in your body. Feeling/looking like a mosquito bite and irritated for days is not right.
Are you comfortable with the way (and the where) to inject... did they show you the correct method in the clinic? I ask because I have heard horror stories of folks sent home on insulin with little more than the prescription.
I'd suggest this is something to discuss with your Doctor and perhaps consider trying another long-acting insulin such as Lantus.
Do you have an home Blood Glucose (BG) meter? How often do you test? What numbers are you getting? Can we advise on diet to help manage your BGs so that you might be able to inject less insulin?
You might click and read this thread
if you are interested in the different ways that Levemir and Lantus work in the body... how it is that a single injection can have an effect over so many hours. I am not recommending one over the other... they have different profiles, different methods of delaying absorption of the insulin and I have read others using insulin find one works for them when the other does not. There are other types of insulin beyond these as well. Options are good!