3wks before my period,i'm constantly having a genital arousal,esp when i'm sitting down or when going to sleep.is it normal?

Normal: Yes - you may be ovulating .

Spontaneous sexual: arousal is not terribly uncommon. It is difficult to link it to specific phases of the menstrual cycle; 3 weeks before a regular period would be before predicted ovulation and not necessarily a hormonally susceptible time. Some have reported positional factors such as sitting where clitoral stimulation might be more likely. There are some treatments; consider an evaluation with your PCP or OB/GYN.