6 month with excema- need constitional remedy?

Have 6 1/2 month old baby boy with excema.

Excema started with vacinnations and intro of solids. Giving cooked veg and fruit and baby rice only so far. Had cradle cap from birth and recurrent thrush in nappy area. Mother suffers from thrush and hayfever.

Excema is under neck, behind knees worst areas. Starting to find small circle patches on chest and back. Rash on cheeks- not sure if excema or from saliva from dribbling and teething. Rash on cheeks worse since weather turned colder. Wakes every few hours at night and needs to feed to go back to sleep most times.

Happy boy, needs a lot of physical contact and attention. Likes to be carried and has started to stand and walk early. Very sociable.Short attention span. Doesnt like to be laying on back. Sleeps on left side. Loves to be standing up most of the day.

I Have tried cutting out dairy, will start to cut out wheat.

Have given Chamomilla drops for teething.
1 dose of belladonna- vomited up- maybe reflux
Beginning Calc. Phos to help teething.

Do I need constituitonal remedy for excema?

reading so many posts on this and now very confused!
Do I stop Leaky gut syndrome? So when do I introduce solids as have to return to work in few months??

Please help before it gets worse. Many thanks.