Is it safe to increase from 10mg of celexa (citalopram) to 20mg after being on 10mg for three weeks?

Yes: Celexa (citalopram) is usually started at 20 mg but starting with 10 mg is perfectly acceptable to see if that dose and medication side effects are manageable. After 3 weeks on Celexa (citalopram) 10 mg it would be fine to advance to 20 mg if you feel that 10 mg is not helping enough with your symptoms.

Up to 40mg: Celexa (citalopram) is prescribed up to 40mg. Some individuals, especially those with high anxiety or obsessive symptoms, will find that their symptoms will not fully resolve until they get to a higher dose, and maximal dosing should be achieved within 8-12 weeks of treatment. If there is little or no response by then, it's time to try another med.