It sounds like she is not really falling asleep. I agree with Meg Stephenson about giving Ibuprofen or childrens Paracetemol to sooth any discomfort (also if this has been recommended by your doctor)
When my daughter was ill I used to comfort her in my arms until she was absolutely fast asleep. I did this because it seemed to soothe her, and I felt better knowing that. Then I would put her to bed once she was totally asleep. The comforting, helps them relax more I think, and in turn this could help them nod off into a deeper sleep.
I still do that now, if she has a cold or feels unwell and feel that it helps. Maybe you could try that and see if it works for you.
Additional note:
There are some really wonderful answers about co-sleeping here. I really feel that a toddler not feeling too well, would benefit from being in his/her parents arms / or sleeping next to them.