"Jacob held my hand while Dr. Snow was sewing, and I tried not to think why that was ironic." I don't understand what Bella means.

Because usually Edward was in Jacob`s place,holding hands with Bella when Carlise o other dctors fixed her.

I was thinking how Jacob,since he is a werewolf,is hot while Carlisle,since he is a vampire,is cold.So it is ironic.
That is just what I thought.

She's remembering her birthday, when she cut her arm, and carlisle was fixing her arm. Edward could barely stay in the room. Now she's with Jacob, in a similar situation, and he has no problem holding her hand because he's not a vampire. Also he's hot and edward is cold. (temperature)

remember the birthday when jasper went at her and she got hurt?
edward couldn't comfort her because there was so much blood.
jacob could comfort her.

it was ironic because before edward left, after the incident at the birthday party, they had an argument because edward couldn't sit with bella while Carlisle was sewing her arm because of the blood and that anyone else would be 'healthier' for her because they could without the urge to kill her. jacob was able to hold her hand despite the blood. she was trying not to think about it because it made her sad to think of edward, that incident in particular.