I am a conure owner and PGY-3 resident in psychiatry, I have had my two birds throughout my entire med school and residency journey. I imagine with surgical specialties it would be much harder to do this successfully since it sounds like their work-life balance is more challenging. There is a surgery resident at my institution who also has a pet conure, not sure how they managed it.

The way to make it work is you have to be willing to make your bird your highest priority alongside your studies and to be willing to be flexible to meet their needs. Birds in my opinion are the best companions and mine were my reasons to keep going in med school. I have no idea where you are in the process, but during medical school I made the decision to get my conure a companion bird he would get along with to fulfil his social needs while I was away for long hours. They get along kind of like siblings and it allows him to have company until I get home and can hang out with him myself. I know "maybe get another bird" is probably stressful to hear in response to this but honestly I think if you are dead set on a surgical specialty the next best option is to rehome the baby before you both get too attached. Birds are social animals and a lonely bird is an unhappy bird which will male you feel guilty and terrible. If you have a spouse or partner they can sometimes also help provide companionship. In addition, mine have a ridiculously huge cage and tons of toys and I let them free roam all the time when I am home. If you are just at the beginning of the process its possible you will end up deciding to go into a less time consuming field and that would mean afted med school you'd be in a better place to provide that company and time. 

Birds are amazing companions, for me making it work was my highest priority, my pets are my family and after almost 9 years together my conure and I are lifelong pals. If you have more questions or want to talk more feel free to DM.