The paediatrician should have just put you on something rather than letting the GP work it out. I found GPs not that helpful with milk allergies and just went with what the consultant said.
We saw a dietician straight away as they can advise on milk. I'm surprised the paediatrician is making you wait. It's the dietician's job to sort the milk out. Especially if they're querying a lactose intolerance too.
If you're bf you'll have to cut dairy and soya out you're own diet too. They say 40% are also allergic to soya and 90% to goats milk so they aren't recommended as an alternative at that age.
Like I said, they usually try a hydrolysed formula first, and if that doesn't work then you move on to a amino acid based formula.
We see an allergy consultant rather than a paediatrician, they have been brilliant.