Is tonsillitis a serious illness?

Not usually. Our first president (george washington) died from a complication related to surgery for tonsillitis but generally tonsillitis is not serious... Other than causing severe pain. Complications include a peritonsillar abscess and severe swelling which can block your breathing. More importantly the streptococcus organism can produce toxins which can cause heart and kidney damage.
Yes. Particularly if caused by strep and left untreated. The bacteria can effect your heart valve and kidneys. Get it seen and treated.