That advice surprises me coming from an avian vet.
I suspect that if you ask your own doctor, they will almost surely tell you not to have birds.. that is unless the doc is a bird person, and gives you guidelines and tips on what to so/not do. Many non-bird people see birds as filthy.
There are some zoonotic (interspecies) diseases which are a concern to humans, but since you’ve had them for 5 years, I “personally” wouldn’t be worried. Adding another, I’d test for Psittacosis because it can make humans very ill. I personally also wouldn’t get another bird now if only for the fact that you’ll be pretty busy upcoming. But it’s your choice.