Hey OP, I'm a paediatric physiotherapist.
Not here to judge or demean your experience at all- plenty of people do take their little ones to chiropractors and some have found it useful.
However, please be aware that it is not recognised as a conventional medical treatment, and in some cases it will be designed to get you to keep paying out money.
If what has been said today concerns you, I would really recommend chatting with your GP or health visitor who can hopefully reassure you.
Babies (and humans generally) are not symmetrical and it's really common for their heads not to be perfectly round, the bones are still soft and taking shape at that age.
As for the weakness, that does unfortunately sound like a bit of a trick, as babies' strength in terms of "pulling up" is mostly a reflex in the very early stages (I'm assuming here that your little one is quite new) rather than developed muscle strength and depending on how she was handled it can easily appear that one side is stronger.
Please be reassured, you have not been sent home with a baby with lots of issues that no one has picked up on. You have been persuaded by a business to pay out money.
If it makes you feel better and you notice improvements in baby then no harm done! And you should definitely do what you think is best for your little one. I just wanted you to be aware 