Without sticking my nose in too much, it is your fmaily and you know them better than anyone, but he´s willing to help you and take your bird to the vet sooner than you are able to go, so I would be inclined to let him. That way your bird gets seen sooner rather than later.
Administering meds is easier than it would seem. Towel the bird, once you have them in a good grip in one hand, use your dominant hand to insert a syringe into the beak (be gentle, don´t force the syringe in) and give the dose (it´s usually a very small amount of medicine), if they don´t open the beak, one drop at a time where the two mandibles meet will allow the medicine to trickle down and go inside, takes a little longer but be patient.
Wait a good 20 seconds or so before releasing after the medicine to avoid them shaking their heads and flinging any unswallowed medicine.
A good tip if you get multiple meds, observe well, and if you notice they dislike one more than others, give that dose last (I have found antibiotics have been the worst for us so I always give those last).