Does this sound like carcinosin?

Hi all. Well I am taking my son to a homeopath and for the first appt I made up this extensive list about my son. His homeopath recommended baryta carbonica a few weeks ago and I saw a few improvements at first but they dont seem to be lasting. I have heard good things about carcinosin for some autism cases. I know that homeopathy is not'one size fits all' but I just wanted to post this on here and see if his symptoms, or some of them at least, sound like carcinosin. I appreciate any help with this!

Symptoms-physical, emotional, mental, personality
He wakes at night often. Seems to get constipated. Suspect possible headaches or discomfort around eyes due to constant poking and prodding of his eyes. Had eczema as a baby
Very frustrated by inability to communicate.
Whines very frequently. Throws tantrums very frequently, sometimes for long periods of time, cannot be calmed down by anyone when he has these.
Gets upset over very small things.
Gets very frustrated when he is not able to do things himself, such as put on his shirt, pants, etc.
Can sometimes be aggressive
Very hyperactive, runs around most of the time, cannot sit still for very long
Can be destructive of house and things around him
Laughs or cries for what seems like no reason.
Can be happy one minute and very irritable the next
Does not listen very well to directions, tends to not pay attention when told no or laugh. Always chewing on everything (especially his shirt)
Likes to climb on everything (chairs, tables, dressers, etc), loves physical play (having dad flip him for example), loves swinging, jumping on trampoline, very sensory seeking
Loves to be tickled
Loves to have his head rubbed or hands placed over his ears, seems to like pressure on his head, likes firm pressure on his body.
Very messy eater (sometimes throws entire dinner on floor)
Constantly getting into everything
Makes huge messes
Will get his own food out of pantry or refrigerator if given the chance, is constantly hungry, craves breads, sweets, salty foods, meats, etc,
Very messy stools most of the time, only firm sometimes
Has a lot of yeast in his system
Can be very defiant and uncooperative (taking him to the bathroom, getting him dressed, etc)
He is easily upset (very emotional at times), will at times be upset when he is told no and other times will laugh or not pay any attention
He is very sociable with therapists and teachers, tends to listen better to those other than his parents
Seeks out teachers attention. He is not as sociable with other kids. Usually likes to work (ABA therapy and other related activities)
He is nonverbal, only babbles and says 'buh' for things that he wants which he learned in therapy, does not really use too many other meaningful sounds, will sometimes point.
He understands a few directions such as 'lets go bye bye,' 'sit in your chair so you can eat,' 'lets take a bath,' etc
Motor skills are pretty good.
Loves riding in the car and being out of the house, loves school
Will sometimes play alongside other kids but for the most part is not very interested in them.
Entertains himself well for the most part
Does self stimulatory activities such as mouthing, spinning, flipping light switches
Loves to play with shoes. He likes to walk around the house in different pairs of shoes and socks.

Vaccinations
Zach received all of his vaccinations.
He was very irritable for about a week after receiving vaccines (MMR and others I believe).