My dentist didn't scallop my whitening trays so they're extending onto my gums. Is this going to cause major irritation?

This is a debatable point.  Every dentist and tech likes to trim the whitening trays differently.  Some scallop the trays some have them extended past the gums and strait across.  More resent studies done by Clinicians Report recommends extending the trays past the gums and not scalloping them.  The extension is supposed to help seal the gel on the tooth and prevent leakage, scalloping can increase the leaking at the gum tissue.  With either tray trimming option used the important thing is to not use too much whitening gel.  Make sure to tap over the front of the tray after you set them in place and wipe away the excess at the top of the tray to prevent gum tissue irritation.  

Sorry you had this experience. It is easily corrected. Your dentist should be able to scallop the edges of they trays in a very short time. Until the trays are scalloped I suggest stopping the bleaching process. Your gums may become irritated.