Immunodeficiency? Or paranoid?

So my little guy is 6 weeks old and can’t seem to keep healthy. He has a hospital follow up appointment in 2 days so I’m going to talk to his doctor about my concerns then.

At 2 weeks old he got viral meningitis caused by the endovirus. At 5 weeks old he got RSV and the endovirus again. The hospital pediatrician said she has never seen someone so little get two serious illnesses and end up in the hospital back to back like he has. She said she didn’t want to dig any deeper by looking into an immunodeficiency at this point and just wants to call it bad luck. Well now at 6 weeks old he has bad oral thrush. I’m now super concerned he may actually have something more serious wrong with him.

Would it be wrong for me to tell his doctor i want him tested and if he won’t test for it I want to hold off on vaccines for awhile just Incase? (Some vaccines can be bad if you have an immune disorder and I would be nervous to give him his vaccines without testing to see if he has a problem or not. I want him to have his shots but maybe hold off awhile until I know he is okay) Does anyone have any experience with immunodeficiency? Am I being paranoid and he really is just this unlucky?

Update-

I asked at his hospital follow up appointment today if he just has really bad luck or if there could be an issue with his immune system. His doctor said he thinks he just has bad luck. He has his two month well baby check in two weeks and I’m going to ask them about delaying his shots until his 4 month check since he has been so sick. He still has crackling in his lungs and his doctor said he may keep wheezing on and off for a few months from the RSV. If he gets sick more between now and 4 months I’m going to ask about looking deeper into it.