It might be the coffee, but it's doubtful unless you are drinking it before you test; fasting blood sugars should be done as soon as possible in the morning and before you eat or drink anything. I really doubt it's the borage oil.
Blood sugars can go up for no discernable reason at all. Being a women, I've noticed that hormone fluctutions have a distinct impact on my blood sugars...usually up roughly 10 points once a month like clockwork during TOM.
Stress can raise your blood sugars. Illness can raise your blood sugars even before you know you're sick. Same thing with pain and injuries. A temporary increase may be nothing to worry about, but it bears careful watching. Since your blood sugars are good the rest of the day, I don't think it's a problem with your pancreas or you'd be seeing consistently higher blood sugars all day.
Your body is definitely less sensitive to insulin (either your own or that which you inject) in the morning hours, so you could simply be seeing the effects of that. You're also going a considerable amount of time without eating anything substantial (from 4 PM until breakfast the next morning) and you may be seeing the effects of a glycogen dump in the morning. You could try eating your dinner later in the day to see if that helps.
I also sometimes have strange reactions to artificial sweeteners and those low carb bars, so that may be something to consider dropping to see what effect it has.
If your blood sugars continue to go up, definitely let your doctor know what's going on.