I want to update, just to share our particular situation - in case it might help someone else.
Tantrums (wild, raging one's anyway) have abated.
After the horrendous night of being up all night with a 1000 demands, and crying - a chat with her Dad - we decided we needed to either take her to the doctor, or get things back on track with some sleep training concepts.
We booked an appointment for the doctor. I monitored her for a couple of days, took her temps etc - and we concluded that she is not still ill. So.....we went forward with the sleep training - which involved visiting her for reassurance to start with, then increasing the time, then leaving her to it. (She is one of those children where intervention makes things much, much worse...so we have to, at some stage, leave her to work it out herself - she has always been like this).
She was a bit unhappy the first night before going to sleep. But since then has more or less gotten completely back on track. We've now had three nights of good sleep again.
She is also taking later naps, or shorter naps, or skipping naps again - rather than taking the very long one's she just recently has been having. Thus, this has returned to 'normal' too. Back to stressing about her ending her naps! Eeek.
I should also add that her appetite, which was a bit out of control there for a few days (I swear she was eating double what she normally does - she had a stomach like a hot-air balloon for a week!) has returned to normal too now.
My conclusion is still that both her behaviour, and her night wakings were related to the illness. I really think it threw her for a loop emotionally. Her behaviour during tantrums, and even at night seems in retrospect to be an angry/confused cry for attention or reassurance. I've been trying to give her lots during the day, and she seems much better.
To those who said she was turning three, and thus to expect more of this - well, you may be right, somewhat - we are having more issues with unwanted behaviours...but these protests and mini-meltdowns, seem 'normal' compared to the insanity of the previous tantrums - so I think they are two different things.
Crossed fingers, things are relatively okay now.