The general name for skin problems of caused by caterpillars
is Urticaria.
In Australia: approximately 1,000 diferent species of moths
have caterpillars that can cause Urticaria.
There are 4 different ways that a caterpillar can cause
Urticaria:

Caterpillars of
Doratifera vulnerans, LIMACODIDAE
with stinging hairs everted.
- caterpillars from the family
LIMACODIDAE
have hairs that sting, rather like nettle hairs.
The hairs are sharp and hollow and contain a poison liquid
which is injected into the skin when they are touched,
thus causing pain and inflamation.

Caterpillars of
Chelepteryx collesi, ANTHELIDAE
with stiff sharp barbed brittle hairs.
- caterpillars of some species such as
Chelepteryx collesi
have hairs that are stiff, sharp, barbed, and brittle.
They can readily penetrate the skin then break off.
So the result of touching one of these caterpillars is
like having a bunch of splinters.
These are especially dangerous if they lodge in the eye.

Caterpillars of
Euproctis edwardsii, LYMANTRIIDAE
with hairs.
- other caterpillars of the four families
ANTHELIDAE,
ARCTIIDAE,
LYMANTRIIDAE, and
NOTODONTIDAE
are hairy, and some people are just allegic to the touch
of hairs from some of these caterpillars.
These people come out in a rash if they touch
a caterpillar to which they are sensitive

Caterpillars of
Ochrogaster lunifer, NOTODONTIDAE
with infected hairs.
- some caterpillars of these same four families
ANTHELIDAE,
ARCTIIDAE,
LYMANTRIIDAE, and
NOTODONTIDAE
have hairs that are sharp enough to pierce the skin,
but the hairs carry bacteria and other micro-organisms,
so these micro-organisms are injected into the skin in these cases.
Depending on the organism involved,
this can result in infections of many different sorts.
For example, mares carrying foals have been thought to have
spontaneous abortions if infected by microorganisms
on the hairs from larvae of
Ochrogaster lunifer.
People can get Urticaria from more than of these causes:
maybe the hairs cause an allegic reaction and also cause infection,
or any other combination of the four causes.
So never touch a hairy caterpillar.
If you want to move a caterpillar :
then put a bit of paper or a leaf in front of it,
and then tickle the rear of the caterpillar gently,
with a twig or something,
until the caterpillar walks onto the paper or leaf,
then take that with the caterpillar on it,
and put it somewhere out of trouble.
The problem is not confined to the live caterpillars.
As the caterpillars grow: they moult and
shed their old (hairy) skin to grow a new bigger one.
The old skins decompose and the hairs can blow about
and cause Urticaria if they land on someone's skin.
Furthemore, when these hairy caterpillars pupate in a cocoon,
they usually attach their hairs to the cocoon,
so touching the cocoon can also cause Urticaria.