What, she wants you to give up a paid job to take an unpaid internship? Or is expecting you to be able to do both? Regardless, it is your decision and not hers to make.
It's okay to be upset by the hurtful comments she has made about you and your illness, you are allowed to have feelings. As you are suffering from clinical depression, its not surprising that you are taking this hard.
Once you are feeling a bit better, I guess you need to think about where you go from here. I think it would be healthy for you to have some boundaries - such as refusing to get into an argument about your career choices. You don't have to justify yourself to her. This is a hard thing to grasp if she has been emeshed in your feelings and decisions up till now, but you really don't have to convince her that unpaid internships are terrible (either in general or in your case). I'm not an expert about how to word these things, but if she brings it up again, you can reflect her view back at her so that she knows you have heard it.
"You think I should take an internship. I am not taking an internship. I do not wish to discuss this further. [change subject]" (and if she continues to try and argue with you, "I said I was not going to discuss this." [and leave].
That said, I think that after the hurtful things she said about you being ill, I think that really you should just try and disengage from her a bit. Hopefully she'll apologise. If she doesn't and just tries to pretend it hasn't happened then just say "You said some really hurtful things to me about my illness/career choices/etc the other day and you haven't apologised for them, so I'm not in the mood to talk about X, Y or Z"
Even if she does apologise, be cautious about her being controlling on these issues or other issues again. Given that you are unwell, it's easy to become too dependent on one or two relationships, do try to get some time away from your mum, preferribly with your DP or friends so that you can have some perspective on your relationship with your mum. Be cautious about the "best friends" thing if this is dependant on you always agreeing with her and doing what she tells you to.
Hope you recover from your illness soon, and that your mum is capable of having a non-controlling relationship with you. Have you had/would you consider talking therapies? they might give you the space to think about your relationships.