Let them sort it out themselves, they will be able to get over it. It's a good life skill to learn in a safe environment. Although I would follow up if DS really isn't pulling his weight and DD is having to pick up the slack.
Look, he's apologised which is great - he was in the wrong but he's aware of it and she just needs to cool down now. In the morning, if she's still giving him the silent treatment have a quiet word with her asking her to let it go - It's not worth a family feud over.
My kids are a similar age. I would let them get on with it. Let them thrash it out, let them have their own relationship, find their own limits and set their own boundaries.
I would speak to the one who lives at home and explain if he wants to live with you then he needs to do certain things around the house. 22 is certainly old enough, I had had a mortgage for two years by that age!
Keep being proud of your daughter, it's a shame others choose to focus on the medical degree as special, I think you can provide the support she needs so she, and others, can see that her chosen profession is just as worthy.
My DC had a big argument tonight. DD20 is at uni and DS22 lives at home for uni. DD has just got a graduate job and is ecstatic. It is a great job, very competitive and perfect for what she wants to go into. She really deserved it as she worked her socks off preparing for the interview and has done so much experience in the field. DS is doing very well too, studying medicine. Family members can be quick to comment how fab he is, how clever etc (I make sure I show them both how proud I am) but I know DD feel a bit of the underdog compared to her DB.
DS made some sarky comments about DDs new job, joking about it mostly. He took it too far though. At the time DD stood up for herself then went very quiet and I could tell she was hurt. Later on, I moaned he never helps clear up while she is at uni and hence it is so nice to have her home as she is so helpful. I meant it more as a compliment to her but she got upset saying how she hates how disrespectful he is to both me and her. She then DD flipped because he was laughing, and she then stormed off to her room.
I told off DS a lot and gave him a strong word about his attitude and how he takes his teasing too far and is insensitive. Also about how he needs to pull his socks up in terms of his contribution in the house. He went and spoke to her and she exploded and cried and told him exactly why she was cross at him. He said sorry and comforted her but she remained very upset.
It is tense, all are in their rooms in silence. DD obviously wants space right now. I've kept out of it as far as possible..