All latex paint contains solvents that can precipitate death in an asthmatic. Whoever informed you otherwise has one brain cell in his left toe. Advise them not to have children.
This is not a minor issue.
Inform your boss that his actions constitute a D felony of reckless endangerment, in case he doesn't get the point.
With good ventilation, all windows open, three-four days should clear the place out of fumes.
Hi Peggy!
I hope you are able to come up for air and get as far away from this situation at work for as long as you're able. It sounds like you may be allergic to some of the chemicals from the paint since latex paint does not have natural rubber in it OR from the actual latex in the masking tape that they may be using protect some areas from the paint, which, btw, is full of latex!
You know, asthma is closely related to allergies and when allergies of any kind are triggered, asthma can easily kick in too.
I found an informative link on this subject which you can visit here:
http://www.latexallergylinks.org/paint.html
Hope this helps and all my best wishes...
Your Friend in Faith