Your symptoms point towards obsessive compulsive disorder (OCD). OCD is a thought disorder and is characterized by obsessive or intrusive thoughts and feelings that can cause considerable distress unless specific repetitive actions are not done to relieve these thoughts.
It can be described as an ego-dystonic type of disorder because you will know that these thoughts are inconsistent with your beliefs and you try to get relief from them by performing stereotypical ritualistic actions like washing hands frequently closing opening doors, repeated checking of locks and personal belongings or in your case felling compulsive to same actions with both hands etc.,
Sometimes people with OCD cope quite well without any major disruption in normal life while others can feel major stress in day to day life. Behavior therapy with techniques like exposure-response prevention and associative splitting is very effective in treatment of OCD. Drugs like Clomipramine and Fluoxetine are often given as part of treatment.
Consult a Psychiatrist for evaluation and treatment. Thank you.