It may have been worse because you had both jabs done on the same day.
My vet refuses to give the dogs more than one jab per visit for fear of not being able to identify the allergen if the beastie should have a reaction. (which is quite common, I understand, and why we are asked to sit in the vets waiting room for a few mins after the appt, in case the reaction kicks in)
Ironic that NHS staff fill us with as varied a cocktail of jabs as possible at a single visit, isn't it?
The difference is of course money.
I pay for the vet's time, and additional appts.
The NHS don't have that luxury.
(getting off my soapbox now

)