One of my kiddos has an allergy and a side effect of that allergy is his eczema flared up. We treated his eczema for over ten years (dermatologists) before realizing he had an allergy.
So what's the allergy to? Have you removed the allergen? That's where I would start? Is it a food allergy? Food allergies cause diarrhea or loose stools.
So I would start there. Eczema could be a result of that. Have you seen an allergist?
The reason I suggest this is because you could be approaching this backwards, as we did. Then you could waste years dealing with a skin condition when you're missing the cause.
I don't think it's a side effect of the Claritin (personally) because it should have happened immediately when he first took it if it would have upset his tummy - not 2 weeks in. That's just my two cents, and experience.
I would check with the doctor or a pharmacist, or even call the Claritin 1-800 number. But definitely ask about seeing an allergist. Better to get to the route of the problem. Eczema (after really going through this first hand for many years) is often a sign of a BIGGER problem - just the skin reacting to some underlying issue.
Figure that out, rather than dealing with it - and you'll have much better results.
Good luck :)
* There are simple cases of baby/infant eczema (I have 2 other children who had that) but it's not so bad that you would need to take Claritin for it. That's the kind that a thick emollient would take care of it. There's a difference.