Could I be suffering from migraines???

I had painful migraines during my pregnancies some years ago, and my grandfather on my dad's side and my mother and my sister all experience serious, debilitating migraines. I'm 40 and have felt like I was lucky to not inherit these migraines, but after I experienced a trauma (PTSD) some years ago, I have been experiencing other health issues, among these, what I call "brain fog episodes":

I have been in and out of offices of neurologists and hormonal doctors and psychiatrists, due to a lot of "systemic" symptoms, such as pains, tinglings, anger issues, confusion, brain fog, speech issues, and wierd feelings of paralysis of my brain and strange swooshing sounds in my ears, fatigue, dizziness, etc.

I myself have linked these episodes to foods I eat, to dehydration, to stress and to lack of sleep. In particular I cannot have caffeine, chocolate or aspartame. Aspartame drives me totally nuts. Like a mental patient, really. I get confused, start to scream at people and then I crash on a bed in confusion with a foggy brain, unable to speak and I just cry and cry and cry.I feel drunk and hung over and depressed and scared all at once. With chocolate and caffeine it feels more like a heavy blanket lands on my head and I have vision issues and feel extremely fatigued/dizzy.

Since I don't have headaches too often during these episodes, I haven't thought of migraine as a possible reason, but the neurologist asked me last time I was there "what do you personally think it is?". I answered "I think I have some sort of allergic reactions to certain foods, and somehow it attacks my brain and not my belly like with others". He then joked "allergies like migraines?", and we both laughed, but after I was there, I started thinking "what if these things actually ARE migraines?

Could I be experiencing migraines? Just without headaches?

I actually HAVE HAD migraines during some of these fatigue-episodes, with auras and half my head in throbbing pain, but I thought of these migraines as caused by the brain fog episode and not vice versa. What if instead the whole brain fog is a migraine, and headaches and auras are just sometimes present? Is that possible? And if so, why haven't the doctors thought of it?

Should I mention this idea to my doctors, who by now probably think I'm just mentally ill (they haven't said it, but I'd think so myself if I were them). I don't think I'm mentally ill generally, but at DURING these brain fog episodes I feel demented and stupid and I get super depressed and aggressive. :-/