I would second (or third) comments from
@EllieM and
@alphabeta that this is likely to be night time hypos. Your morning high may be caused by your body overreacting to its recovery and dumping too much glucose.
I have also seen a few people comment that they experience something similar when their BG goes high. I think this is less common and, as a newly diagnosed person with type 1, your body is likely to be more familiar with highs.
The only way of telling is to take a BG reading in the middle of night (you could set an alarm to wake yourself) and respond accordingly.
If this is happening regularly, you will probably need to adjust your insulin dose. There are many contributors on the forum who could make suggestions but, if you are in touch with your diabetes team, they are best placed to advise which insulin and by how much.