“Does removing adenoids help sleep apnea?”

It depends on the individual, and what other factors you may have relative to your diagnosis. That's unusual for your age, I would see an oral surgeon to make sure this is not relative to a malposition of your jaw structure.

If adenoids and tonsils are large (kissing tonsils), then one could go for in-lab sleep study (not home study). If these are causing upper airway obstruction, removal of tonsils and adenoids would help. If symptoms persist, a repeat study in 3 months be done in-lab to determine the need for positive pressure treatment.