Sorry , I was wrong . In Wikipedia on levothyroxine page they say The effects of overdosing appear 6 hours to 11 days after ingestion
So , I think , 36 hours can be the right answer to your question .
I second Goolarra's advice (AND concern) without taking your Levothyroxine for this 10 day period of time. You would experience hypo symptoms within a 36hr period (at most) but keep in mind that the LESS optimal you "WERE" with your condition the WORSE you will feel with your symptoms coming back and you would experience them quicker if you were not optimal prior to stopping the med.
Your question basically asks: What side affects should I experience?" - (not taking your meds for nearly 2 weeks. To intelligently answer that one should assume you were NOT optimal with the condition so in simple terms the side effects can range:
Mild= inflammation, headache nausea, IBS, acid reflux, sore joints, aches and pains, swollen face, sore swollen gums in mouth, vision issues, mentality or "fog" thinking, ringing in the ears, to mood changes, behavior and absence or worsening of your cycle.
Severe = all of the above + Heart attack, stroke, coma and DEATH!
You will almost certainly experience some return of hypo symptoms. Lethargy is a symptom of hypo, but vomitting isn't a typical one. Are you back on meds now?
I think 10 days are not enough to feel some change in the symptoms . Meanwhile you have to get back taking the meds , in the same dose every morning .