Do you mean that you have only tried 4 PICC insertions total? If so, aren't you still working with an experienced PICC insertor?
Yes, you are correct to remove needle from an artery ASAP and hold pressure for quite some time (10 minutes can be used as a guide).
To be frank, I'm concerned at someone trying a Brachial vein, with little experience, unless they have confidence that they can access the vein without difficulty. I'm not trying to put a damper on your PICC inserting, however, worse than bruising can occur when in the Brachial bundle.....like permanant nerve damage.
Do you not have some Medical Intervention available for back-up? If this person only has a Brachial vein to use, not Basilic or Cephalic, that may be best.
Using the same vein immediately may not be ideal, however, we deal with reality, not ideal. As you said, PICC was removed as it was thought to not be needed, not due to infection or thrombus, so placing it in the same vein may be necessary.
By the way, when accessing the Brachial vein, it sometimes works best to enter a bit to the side of the vein (away from the artery and nerves of course) and then angle over into the vein.
Hope that helps.