I'm sick now, too. I have a sore throat, hacking cough, some sneezing, the shivers, and a runny nose. I went to a doctor and she called it "a flu-like illness." I've never heard that term before. You can read how I'm dealing with my increased insulin needs.
I can't give you any advice on how my pump experience translates to MDI. My basal rates have been as high as x3 my normal rates for 8-12 hour periods. I use a CGM so when I start getting some low alarms (<70 or < about 4 in your system), then I reduce the basal rate to x2 or normal. My BG control has been very good on this aggressive basal regimen. You can't do this on MDI. You'll need to experiment and keep close track of your BGs. Keep good records. My memory and brain aren't working too well.