In House MD season two, there was this girl who was immunocompromised and developed neurological symptoms after having a tick on her. Does that really happen if I get a tick?

It appears you are referring to House MD Season 2 Episode 16 “Safe.” The final diagnosis was “tick paralysis.”
Tick paralysis is caused by a neurotoxin in the tick saliva and is commonly associated with the Dermacentor andersoni (wood tick) or Dermacentor variabilis ticks (dog tick) that are found in wooded areas. After a tick attaches itself to a host, it begins to release the neurotoxin into host’s blood stream. Symptoms typically begin 5-6 days after a tick attaches to a patient with numbness and tingling in the lower extremeities that rapidly progress to weakness and paralysis of the entire body over a few hours to a few days. Removal of the tick is the mainstay of treatment and symptoms can be expected to resolve within hours.