No, do not self diagnose yourself with anything. You can't self diagnose yourself with cancer, or with anemia, or with allergies, or with anything at all. You need to be medically evaluated by someone who has spent 12 years in medical school to properly diagnose anything. You said you are shy, that doesn't automatically mean something is wrong with you. And taking online tests don't mean anything at all. My niece just started talking at 3 years old - I think that's more common than you might realize.
I like routine as well, you might just be a type-A personality. But I'm not a doctor, so you should talk to one. How can you be 100% sure about having AS if you haven't even been tested for it yet??
Noticing patterns is normal, and doing something 3 times sounds like OCD not AS.
Also, you said you're very empathetic? People with AS have said that they have a hard time relating to other's emotions.
I'm just pointing out that the reasons you've listed do not automatically mean AS.
My sister came home from work one day crying because she convinced herself she had aspergers, we had to convince her that she was totally normal. She claimed she met all the criteria for it on some website, and she was convinced she had it because she "was obsessed with dinosaur toys when she was little".