At this point your budgie is still in the process of adjusting to the new environment as well as his new family. You can help your budgie in feeling more comfortable by covering the cage on 3 sides (leaving front part uncovered) and having some soothing music on low volume for him.
Getting a 3rd budgie would only make things more complicated when it comes to housing them on the same cage. More often than not, this number will not work, because one budgie would necessarily be left out, the potential for fights to happen is higher too.
For your situation, it's best to keep things as they are now and stick with a total of 2 budgies.
It's good that you will be taking your budgie to the avian vet for a check up.
If he gets the all clear from the vet, you can then move the newbie budgie's cage in the same room of your other budgie and start with the slow introductions.
Be sure to read this link for the detailed information: https://talkbudgies.com/new-budgie-ar...o-budgies.html
Best of luck with your new budgie friend!