Is it possible to get addicted to Ativan after only using it 2 to 3 weeks?

In a word, yes.  You are not addicted in the classical sense, but have developed a dependency.  The rate at which this can occur is highly variable.  In your case dependency is more likely because you took a relatively high dosage.  Fifty 1 mg tablets over 20 days comes out to more than 2 mg a day.  I imagine that it made you really sedated at first.  I would have started a new patient on something closer to 0.5 mg once or twice a day - or even less.  Withdrawal symptoms tend to peak at around 48 to 72 hours.  Then it typically will remit over the next week or two.   I suggest that you call your doctor and get a prescription for a few 0.5 mg tablets and some tapering instructions.