Is it true that wheat in my diet causes my brain to swell thus contributing to my depression and migraines?

No. Migraine is a neurological event. One's brain does not swell during migraine. The genetically impaired brain will become sensitized by a trigger resulting in the release of neurotransmitters which will turn on pain, light and sound sensitivity and impaired thought. The migraine event may last for up to 5 days. Www. Ache. Org.
Wheat migrains. Not likely unless you are allergic to wheat. If you are allergic then you may have many different types of reactions. See your doctor to be examined for possible allergies.
Not really. However, if you are allergic to wheat, you could develop an allergic reaction such as swelling of the mouth or throat, nasal stuffiness, rashes, diarrhea, or even anaphylaxis.