The best piece of advice I can give anyone about being socially anxious is this:

To keep in mind that every person on the planet is concerned with their own 'stuff'--their own worries, concerns, problems and most are so focused on that/those that they are not in a frame of mind to criticize you.

I appreciate a bagger who takes a look at the person whose stuff they are bagging and at the stuff they have purchased and bags accordingly. I once had a gal put a raw, dripping package of chicken into a bag with a mesh bag of fresh apples. Yikes! So unsafe and unsanitary. Many young men will bag all my canned goods together. I'm an old woman, I am no longer able to carry a 10-20 lb bag. I finally said something to one of the guys and he (and the checker) said, enthusiastically: "Yeah! Canned goods with canned goods!!" And I said, "Please, not for an old woman!!" So you want to abide by your company's rules (and they will have rules about bagging) but you want to be sensitive to the customer (so they will come back).

When the interviewer asks, "What will you bring to this job?" you can say: "A willingness to learn. An ability to take constructive criticism. A desire to please the customer so she she/he returns to shop again and again. A desire to be a team player--to be helpful to my fellow employees and supervisor. Timeliness: I show up on time." If you can add a nice firm but not tight handshake, a friendly smile and a listening posture with some direct eye contact while the other person speaks, even better<-- right there is all you need for entry-level work -- and work in general, if you ask me.

As an employer I am not worried about someone being socially awkward, or having autism, or having a mental health problem, or having a physical health problem or having zero experience--I have hired and supervised all kinds of people along those lines. So go into your job hunt with the attitude that if the place is advertising entry level positions they won't expect you to have CEO-level experience, and you don't need to disclose all your personal stuff (frankly, most of what people have as personal challenges shows, anyway, to the person who is compassionately looking)--you only need to have the mindset of what I have put in bold type. Good luck! The fact that you cared enough to ask this question shows you are the kind of employee I would want to hire.