What is she laying on for bedding and outside? Could be a contact issue with some material, grass, etc.
Definitely she could maybe have some little critters nesting in her bed?! (Yikes!) And she could be picking biting insects or mites up from the grass outside if she lays in grass. A short-legged small dog like a Shih-tzu is also closer to the ground when just walking.
You could try spraying her bedding with PRESCRIBED flea treatment (not an over-the-counter one, as some have been found to be toxic, even though they are cheaper) -AND then boil-washing it afterwards. Make sure there are no traces of detergent or fabric conditioner in it when it is rinsed. So make sure it's rinsed very well.
What sort of food does she eat? Is it good quality, with meat/fish as the first ingredient -and NO corn, additives, chemicals, by-products, fillers, or colouring? If not -switch her diet to something more natural and healthy, or home-cook meat and vegetables for her, and add a vitamin/mineral supplement designed for dogs. You an also add a recommended amount of Omega-3 oils.
Dogs don't literally sweat through their bellies, as they can only lose heat through panting, or a little through their feet. But if she feels hot and sticky, it might be from licking the irritation.
Also, what cleaning substances do you use? On floors, etc. Could she have got some of those chemicals on her? Changing to a steam cleaner (only using water!) can make a difference if dogs react to household chemicals. In fact it's a great idea where pets are around. Steam-cleaning gets to very hot temperatures and is very hygienic, killing most germs.
Has your vet tested her for a staph infection? It's pretty common for a staph infection to manifest itself as itchiness, redness and rashiness in the belly/groin area. Antibiotics and/or antibiotic creme is what is prescribed for this. Maybe try another vet or ask your current vet if they feel it might be staph? It sounds to me like this is what it could be since things that should soothe a rash that comes from an irritant don't seem to be working on her.