Welcome! And congratulations on your new little guy! I am sorry for the loss of your shih-tzus - losing our babies is always so hard. But I am so happy that you have opened your heart up to this new baby, even though he was such a surprise! You will all adjust soon and it will be like he's been there his whole life.
I would definitely make an appointment for him in the morning - things can happen and change so quickly and its not worth the risk of hoping he will get better. It's better to be safe than sorry, so I would definitely recommend having him seen asap. Prayers that everything is a ok and that this sickness is only him adjusting to his new home/diet/environment. Best wishes to you and your new baby!