I've recently done a lot of reading about different insulins and their profiles etc., but I've not read anything that suggests insulin in itself can cause depression as a side effect. In fact, other than potentially allergic reactions at injection sites and the potential to cause hypos, there is very little in the way of side effects from insulin, much less so that other diabetes meds.
I think, as nosher said, a lot of aspects of diabetes itself can cause depression and difficulties coping, but I don't believe that any particular brand/variant of insulin, in itself, can cause it.
This is perhaps a conversation you need to have with your diabetes care team.