Sty/chalazion in upper eyelid during pregnancy: Can I get surgery to remove this? (Photos)

I developed a stye in my upper eyelid a month ago. I was put on cephalexin for a week, along with erythromycin. It's better and not painful anymore but still hasn't gone away and looks bad. I'm also pregnant. Can I get surgery to remove this? Will surgery anaesthetic be safe during pregnancy? I've tried various natural remedies such as warm compresses but nothing is really working.