I'm sorry that I'm unable to help with specific doctor recommendations (I'm in Canada).
Many of us rely on a team of doctors to manage care including, 1. A doctor in internal medicine as your primary care physician (preferably one with links to a medical University), 2. A hematologist and 3. An immunologist.
With your son only being 3 months old, it would be important to find someone in pediatrics as well. If you have a local children's hospital, try looking for a pediatric immunologist or hematologist.
There is no known cure for SCLS, but some SCLS sufferers manage their condition with Theophylline and Terbutaline therapy. For my husband, those medications did not work at all. He now gets monthly IVIg transfusions, which have significantly reduced the amount of SCLS attacks he has. But, he still has episodes now and again that require hospitalization.
I don't know if any of these therapies can be used in someone only three months old, so you should definitely discuss it with someone in pediatrics. A pediatrics immunologist would have experience with IVIg and children, and would thus be a far better choice than a regular immunologist.
You should know that IVIg transfusions are very expensive and are used "off-label" to treat this syndrome. It often means a battle with the insurance companies to get it covered (if that's an issue where you are). You should also know that there can be some pretty severe reactions to IVIg therapy, so it's definitely not a treatment path to be taken lightly.
More about this disorder and possible treatments can be found by clicking "Disorder Resources" in the menu at the top left of this page. Much of the info is based on the experiences of adults with this syndrome, as it's thought to be extremely rare in children. The yellow links on the left-side of the table will bring up documents that you can read.
Also, don't be shy about printing that info and bringing it in to your doctors. You may find some doctors get offended, but most welcome any info they can get as it's such a rare condition. (The ones that get offended aren't doing you any favours).
I wish you the best of luck, and hope your little one's condition improves soon.