Good for you, do not give up on this little guy just yet until you get a 2nd opinion AND a diagnosis AND some form of treatment!!
it will help if you can get your hands on some reptaboost in the meantime while you wait for a vet, if he is completely off foods and showing no interest- reptaboost may help keep him nourished until the vet can find out what his diagnosis is.

There is a couple reasons why he could be skinny.
So you want to ask the vet to narrow down the reasons.
First ask for a fecal test to check for parasites - if this is the cause they will prescribe you a dewormer.
If he is throwing up foods you will want to check for a disease called CRYPTO. Crypto is a more severe disease that leos really suffer from

MBD is something that will require more attention and medications with your vet and can lead to life long issues with walking/hunting but it is treatable to an extent! For the record this does not look like a severe case of MBD to me although his front 2 limbs are slightly deformed, but I am not a vet or experienced in MBD related issues- , I have just spent a while on this forum learning!
I am hopeful this guy will bounce back. good luck to you both.