Hi A.,
Funny you should bring this up -- I just authored a research article on this topic which was published in BioMedCentral Infectious Diseases Journal (took a full year of the most painful peer-review process I have EVER experienced!)
There's nothing to worry about. In the developing world, most kids have had an Epstein-Barr Virus (EBV -- the virus that causes mono) infection before the age of 6 and never even notice it. In fact, major symptoms and severe sequelae (secondary complications) are rare before the age of 10 in general. Most kids under the age of 10 have very few, if any symptoms, and any symptoms they might have are usually minor and aremildly flu-like. The disease doesn't last nearly as long as it does in teens and adults, but kids still gain full, life-long immunity.
In the industrialized world, a large segment (50- 79%) of the population isn't exposed until adolescence or early adulthood, although only a third of those infections actually result in full-blown mono. In fact, EBV infection typically only causes actual acute mononucleosis in this age group. Even though the disease can seem major, considering the fatigue, sore throat, and swollen glands that accompany it, it's really quite a minor illness in the grand scheme of things. Problems can arise however, such as enlarged spleen and/or liver, that can require the infected person avoid contact sports for several weeks for their own safety, but more severe complications are very, very rare. Considering how badly teens and adults are affected by the illness, however, and considering how much school/work time can be lost because of it, you should be happy if your little ones contract the illness now and get it over with. The only way this would happen, however, is if your kids shared saliva with the sitter, such as by sharing a spoon, ice cream cone or drinking glass with her, or through mouth-to-mouth contact, such as kissing (hence the name, "kissing disease").
Your doctor, BTW, is actually wrong about the ability of adults to infect children with EBV. Most infections are actually probably passed this way, as EBV stays infective throughout life, even after symptoms have completely resolved and the infectious person is themselves immune. This is likely the reason why most EBV infections occur in childhood, and only a small percentage occur in adolescence and beyond. If you ever had an EBV infection and shared eating or drinking implements with your child, chances are good that you've already given them the virus, they had a minor illness, and are now immune.
In any case, since your sitter was most contagious for 1 - 2 week before the symptoms showed up, it's really too late to worry about it now. However, if you've never had mono, you may well be at risk, but only if you have shared eating or drinking implements with her. If you think you might have contracted mono, or if you would like to find out if you have already had mono and are immune, you can ask your doctor to test for EBV VCA IgM, EBV VCA IgG, and EBV EBNA-1 IgG antibodies in your blood. If you have never been infected with EBV all three tests will be negative. If you have an active infection and it's early in the infection, EBV VCA IgM will be positive and the two IgG tests will be negative. If you have an active infection and it is later in infection, usually EBV VCA IgM and IgG will both be positive, but occasionally only VCA IgG will be positive. If you have had a past infection, both VCA IgG and EBNA-1 IgG will be positive and VCA IgM will be negative. On rare occasions, the test will give other patterns, such as EBNA-1 IgG positive without VCA IgG being positive, or all three tests will be positive together. When that happens, the test should be repeated. However, keep in mind that 97% of the population, worldwide, has been infected by EBV by the age of 35. There's a odds are well in your favor that you already have immunity.
The old monospot test is reliable only if you have an active infection. If you want to determine if you're immune to EBV or have never had the infection, your doctor will have to order the specific antibody tests (called immunoassay or ELISA). Frankly, I wouldn't worry about it unless you develop symptoms that persist for 3 or more weeks.
Sorry -- this is probably more than you wanted to know, but considering that b***dy paper took almost 3 years of my life, I figure I might as well share the knowledge!