I feel betrayed by my ex dating another person.
Why do you feel betrayed by your ex dating another person?
Because I don't think she should be dating someone so soon after our relationship ended.
While it is painful to experience a breakup, you have to realize that your ex has moved on and is now free to date anyone that she chooses and you shouldn't be concerned with her actions. If you're having lingering feelings regarding the relationship, you should try to move on as best that you can. If you are unable to do so, it would be a good idea to work with a therapist to process what happened in your relationship and find healthy ways to resolve the negative emotions you are experiencing.
I feel betrayed because I still love her.
I know you must be hurting over the loss of your relationship but you have to move on. Both of you have the right to date and you should consider moving on since your ex has moved on with her life.