What can I say to her to make her feel better?

I have met a person I think have social anxiety. I'm a 33 year old male with social anxiety. Some days is so bad I can't even leave house.
At work there is a girl, who don't talk. She have the same face all the time, she never shows any expressions/emotions, she avoids eye contact, and keep for herself. She often sits alone or with one other person at lunch. I'm pretty sure she has social anxiety.

I am just shocked, how a young beautiful girl like her can have anxiety. With her looks she could have whoever she wants.
I have been trying to be nice to her, but since I have anxiety myself, it's hard to talk to other people. I always says hi to her when I see her, and she does say hi back. When I see her at breaks, I use to go sit with her at the same table. However we don't talk much. She have not giving me any indications that I'm not wanted, so I do think she likes that I try to talk to her. But what can I say to her? I very affraid of doing something wrong, offend her or hurt her feelings.

I asked my psykologist today if It's ok to give her complains about her looks, but she reconnemended me not to do that.

If I told her she has a beautiful face, do you think she would get upset or mad at me?
I'm not in love with her or anything, but she's really good looking, and I want her to have better self-esteem. I want her to feel better. But what can I do?

I wouldn't compliment her on her looks. If she has SA it might make her feel more uncomfortable. Just try and have casual conversations. Start with talking about the weather or current events. If she starts to open up you may learn of some of her interests and you could talk about those things.

You could even talk about what your eating for lunch. And looks have nothing to do with a person having social anxiety or not.

Telling her she's beautiful might scare her off, because odds are she's self-conscious about her looks and thus sensitive to the topic. Just talk about random things you like, movies, tv shows, music, things you like to do in your spare time. Show interest in the things she likes to do, ask her how she likes to spend her time. Maybe the best compliment you could give her (right now) is just telling her you enjoy spending time with her and having lunch with her, etc.

Eventually, if you feel like you're receiving good feedback from those conversations, and if you feel as though she's trusting you more and more, maybe you can take note of things you have in common (from all the conversations I mentioned earlier) and ask her if she'd like to go for a walk on a weekend, or go to some event with you, or go out for icecream, and so on.

Try talking to her about the job like what she thinks about it and stuff like that.