Unfortunately, this is the consequence of cortisone injections.
When I have had them, I have increased my basal insulin for a few days. I had to keep a close eye on my BG to ensure I didn't over do it and to notice when my BG was coming down (it coincided closely with when the pain started to subside) so I could bring my basal insulin back to normal. But raising the basal insulin meant I had to do less bolus corrections so, for me, I found this better. It also helped keep my BG under a bit more control when I was not able to correct (e.g. when I was asleep).
The last time, I had cortisone, I think I increased my basal by about 30% for 4 days.
I hope your knee starts feeling better soon.