Am I right in understanding you are on 4 basal and 1 bolus only with Tea? So a total daily dose of 5 units?
If that's the case, then a correction of 2 units does seem comparatively very high. That could be the reason for the lows - over correcting. And you might be much better off with a half unit pen. Are you just going hypo after corrections to combat the highs?
As for what's causing the highs:
- when you are getting levels of 13/14 what have you eaten and when? Maybe you need to add in a bolus for that food?
- the symptoms you described could be due to hyperglycaemia. Or, you could just be coming down with something entirely separate and that illnes is pushing your blood sugar up?