J.,
a 2 year old does not understand the concept of lying. if she has she has a headache there's something up there and you need to address it.
getting a CT scan is not the worse thing that could happen. my kids have had CT scans. so, if i were you I'd go back to the pediatrician and say you are not comfortable not addressing this and that you need her to give you a referral to go to an imaging place and see what's going on. also the ped. needs to order blood work as well, and take it from there
from experience pediatricians not always are on top of things. unfortunately sometimes it's too late to do something about it. considering i have had to call numerous times for one issue and always been right in the end now they do not take my child' word for granted any longer.
here's an example. a few months ago my two year old said my tummy hurts. this was the first time EVER she has complained of pain. i took her to ped. he checked her (ear, nose basically nothing) and said all clear. a day later she develops a fever and still says tummy hurts. i called the ped. and he said probably just a cold, give motrin. i spent that night trying to lower a 104.5 fever and to no avail. took her to ER and turned out she had strep, and was explained that strep can cause problems with kidneys hence the 'tummy ache.'
now your child does not have a fever but is trying to tell you her head hurts. do something about it
good luck
vlora