@catapillar and
@azure have provided some great advice.
I have a few more thoughts but before I start, I hope you are feeling better now.
The great thing about a pump is the basal should match your basal requirements at all times of the day. For example, our night time basal, whilst we are not exercising or thinking or using up much energy, is typically much higher than during the day. When on MDI with a long acting insulin, like Lantus, that works for up to 24 hours, the dose was really calculated on what was needed over night. This means that during the day, there would be some spare Lantus (or whatever long term insulin you used) in our system to mop up some under-counted carbs. This spare is not available on a pump. Therefore, if we under-count the carbs, it more obvious and, as a consequence, we may be more likely to go high.
As I've noticed these occasional highs on a pump, I have noticed that I need more insulin to bring them down. For me, when I have a BG over 15, I double the corrective dose regardless of ketones.
I have also noticed that my body is not great at taking more than 10 units of insulin in one dose. No problem, combo-dose is here! Basically, if I need more than 10 units, I use the combo option over an hour.
When my BG does get above 15, my finger-tips come in for a pounding. Test, test, test, correct, correct. correct, test, test, test, correct ... until I start seeing my BG come down.
I have had my pump for 18 months and keep learning something new about it and making little adjustments on how I use it. No wonder you are still learning after 4 or 5 months!