As a T2 on insulin, I've experienced all sorts of weird readings in the last month - but I would never make changes with my insulin dose without talking it over with my DN first. When we chat, which is every Friday at the moment, we'll agree a course of action for the week ahead, with contingencies of how I might make minor adjustments, depending on the results I get.
The only significant adjustment I made on my own was when I stopped it entirely when I was away from home recently and having several hypos a day and she wasn't available to talk to for a couple of days and the other DN was off sick. When I told her subsequently she concurred I'd done the right thing, but that's the only decision I've made without her and I was with my sister who is a senior clinical nurse who encouraged me that stopping was the safer option - in the circumstances.
As it happens, my recent experience is similar to yours, in that I was having hypos and in between was going very high (double the figures of the week before), which was suggestive of too little insulin overall. But actually, when I reduced it, the range narrowed significantly. At present, having stopped for a few days and titrating it back up VERY slowly, I'm currently on a very small dose, yet my BG is lower overall with a narrower range than when I was on much more. It appears that with too much, I go erratic, rather than just low - some sort of rebound effect - so I'd worry that you might be the same and actually increasing your dose might just make things worse.
Whilst high BG is far from desirable, it's preferable from a safety point of view to plunging too low - maybe at speed if you double your rapid. So it would be my advice to take professional advice before changing anything - certainly before increasing it.