Does an ige level of 582 (normal 0-100) indicate chronic protozoal infection (or some other infection)? if not, what does it indicate? on electrophoresis i was free of m-spikes, but don't know if that looked at ige, so is ige myeloma possible too?

No: Allergic diseases , especially eczema, are more likely to be associated with an elevated IgE level. Do you have symptoms which prompted the IgE measurement? As far as IgE myeloma, it is very rare condition and the level is not high enough for making this diagnosis. If you have no symptoms otherwise, I would just monitor your progress.

Nonspecific: Serum IgE is extremely nonspecific to any particular problem, and may be elevated in allergic asthma/rhinitis, yeast infections, HIV infection, and tobacco use, among many other conditions. Many other factors in your history, exam, and testing would be necessary to make a proper diagnosis.