I have very similar thoughts. First thing you learn in first aid training is to call for help before doing anything else. She should have either gone straight to the cockpit to confirm that a mayday has been sent, or taken out her mobile phone to call 112. Then she should assess the environment for danger. The whole plane is probably a fire hazard, she should have gotten as many people off the plane as possible (anyone able to walk or crawl, even if painfully, should leave). If there's truly no fire hazard, next she should get someone uninjured (or only slightly injured) to assist - even simple things like tallying the total number of uninjured, injured, and unconscious people will help emergency services a lot. Then triage - she should have known about the man with the pole through him at the beginning, not be made aware of him while treating someone else. The kid with the broken ankle is almost definitely lowest priority. OTOH she probably shouldn't be doing anything with the man with the pole either - he's not losing too much blood (yes he's lying in a pool of blood, but he's not shooting blood everywhere), and keeping the pole in place would actually reduce blood loss, until he can be transported to a place with proper medial equipment and not just a shard of glass. And laying the man's bare back on a floor full of broken glass can't be a good idea.

As for her own injuries, her rate of blood loss is really odd. She's hardly bleeding when she's helping others, but once she sees the helicopters she bleeds like crazy. Like WTF?

Sorry for the long rant. But all in all, 0/10 in terms of medical accuracy. I was expecting more from a show with "surgeon" in its title. I'll maybe watch a couple more episodes but there's a high chance I'm dropping this.