Many years ago, I was told by my boss that I always looked like I had the weight of the world on my shoulders and that I needed to lighten up a bit. Honestly, I was pretty hurt. I mean, I was new and there was so much to worry about and what if this happened and what if I didn't know enough and what if I forgot something and what if this and what if that and I DID feel like I had the weight of the world on my shoulders!
Anyway, after I thought about it for a bit I realised she was right. Nurses don't have to swashbuckle around the ward with a devil-may-care attitude but not everything is an emergency, not everyone is going to die right this minute, and it won't be the end of the world if I don't know every single thing there is to know. I made a conscious effort to try to relax and smile a bit more and it really did help. It was an act at first but soon I was feeling more relaxed as well as looking more relaxed and I found I actually started to enjoy work and even sometimes have a bit of fun. There's plenty of terrifying moments to go around, it's good if you can smile and joke with your patients and colleagues when it's appropriate.
You may not be thinking that you're too proud to ask for help but is it at least possible that you are giving that impression? If what you've said are the only things they found to criticise, I'd let it sink in for a day or so, think about it again without feeling that you're being judged, and then take it on board. It doesn't sound like bad advice to me, and it doesn't sound like a reason for resigning either. :)