To break out in
 

to break out: in a rash
in tears
in laughter.
in a sweat.

Can you use the verb romper (romper a risa etc) ?

Some proposals:

To break out in tears -> romper en llanto / estallar en lágrimas

To break out in laughter -> romper en carcajadas / reírse a carcajadas / soltar la carcajada

To break out in a rash -> salirle salpullido/sarpullido a alguien

To break out in a sweat -> (comenzar a) sudar

Thanks!