There are a number of things that could cause a web-like rash. The answer could be heat rash, scabies, vasculitis or something else. Your best option would be to consult a doctor.
Depending on the onset and development, location of the rash, it can be late stages of immune mediated conditions such as psoriasis, dematitis, eczema.
It could be rosacea or just a bunch of varicose veins coming together. Go to the dermatologist to know for sure. Otherwise, it is hard to predict the exact skin disease.
The rash that has a web looking appearance is called spider naevi. If you have multiple of them on your chest or trunk, it could be one of the sign of chronic liver disease. These rash appeared as a result of portal hypertension which means high pressure within your veins in the liver circulation.
