I was told that as well.I certainly felt it go in!
I normally just suffer a sore arm for a couple of days but this year I've felt absolutely awful.
Both DH and I had the Moderna in one arm and 'flu in the other(I'm 67,DH is 70 and technically the Vulnerable one).By Day 2 after,I couldn't raise either arm above my chest and I couldn't sleep(side sleeper) because of the discomfort from the injection sites.I tried rubbing Voltarol on both to try to alleviate the pain a little,which seemed to help,but not enough to prevent pain when pressure was applied.
DH - experienced a bit of arm discomfort and a brief temp.spike,but otherwise fine.
For me,On day 3,the injection pain eases and is replaced by the classic symptoms;lethargy,feverishness,scratchy throat,headache and a permanently runny nose-it's been like a tap.
We're now on Day 6 and I'm only just starting to feel ok again.I've just spent a week feeling as though I've been "going down with something"; getting on with things,keeping the symptoms under control with paracetamol,but all the time feeling very sub-par.
I wasn't aware that you could ask to have both in one arm;on the website it explains that you will be given one shot in each arm if you have both done at the same time.
Yesterday,while Googling all these side effects-which I have never experienced before to this extent apart from a little arm soreness -I came across a few articles pointing to research which suggests that having both 'flu and COVID jabs at the same time can increase immunity against both.I'll see if I can find the links again.