Send updated resume? Avoid Background check issues? A bit scared... Help....

Hi All,

So I'm a bit spooked. I am currently recruiting for IBD SA 2021, have one superday coming up (date unconfirmed but final interview was promised), applied multiple places, and have recently sent an MD at GS/MS/JPM my resume, which he has graciously offered to forward. After sitting down and reviewing my resume just now, I have noticed some red flags that might cause trouble during background checks.

1) I had a marketing internship and have incorrectly listed the products' (which I was marketing) COMPANY as my employer. Stupid me. It's a big corporation; the marketing firm is smaller and regional. I must correct this, as in the event of a background check, my resume will list my employer as X when my actual employer was Y. This was a genuine and stupid fuck up – I spent most of my days working with company X products, but was getting paid commission through Y.

2) Unpaid internship this summer – is extremely informal, brought on by networking alumni who agreed to give me a "self-directed internship" after I told them my internship was cancelled. It's listed on my resume as an internship, but with how it seems to look (I am starting in July) I'm basically doing self learning with resources my supervisor at the firm is providing. Not really any value-add work to the firm associated; therefore should I list this as an "Apprenticeship"?

I've been browsing background check threads, and have seen the due diligence that firms use, even for SA roles, in the process. I'm extremely worried about #1 in particular and know it must be addressed (#2 less so, as although it is informal and unpaid, my supervisor would provide reference/offer his contact info to verify my participation).

How should I go about correcting this? In regards to the MD, I will email him promptly in the morning with an apology and updated resume (I sent him my resume yesterday and he said he would forward within a week...) For the firms I applied thus far, should I wait to see if I make it to superday then provide my updated resume? For my upcoming superday, should I wait until I'm given the date from HR, then send over my updated resume?

Either way, I do NOT want to be flagged for being dishonest for really dumb mistakes. It would be a nightmare to have gotten an offer, only to have it rescinded. I have applied to primarily only BBs and am aware they have rigorous background check processes. Help?