If you usually run your BG a little high but have recently been hypoing severely, it looks to me as if you need to do some investigation towards what is causing your BG to go up and down so much. Is it your insulin to carb ratio? Do you need less insulin after exercising? Have you been stressed recently? Are you more likely to hypo at night or during the day? ...
After a bit of pushing, my diabetes team provided me with a blind (I couldn't see the readings until they were downloaded) CGM for a week whilst I kept a food and exercise diary which gave me an insight into what was happening.
This provided very useful information to adjust my Novorapid and Lantus. For example, my ratio is different at different times of the day and I moved the time I took my Lantus.
If your team are unable to provide a CGM, this may be a good reason to trial the Libre which will provide similar information. The manufacturers are really pushing it so you may be able to get a free trial. If not, the investment of one sensor could be offset by the value you get by achieving better BG control.
If you still find problems, your local team may be more open to considering a different insulin.
Good luck.