Thanks for all your feedback. It was much appreciated.
I called UCAS - she looked through my form and said that there was no additional information that I could have put on my application that is not there already. My GPA was something the universities were supposed to ask me about but haven't.
I did call the admissions office at both universities. The one at LSE was not very helpful, they told me to send them a "request form" and they would get back to me next week. I do not see anything coming out of it, but I am giving it a shot!
But the one at QM was very helpful. She told me that it sounds like they misread my application. That the reason I was rejected was based on my high school grades, and that I should have received an email (which I did not) asking for my university grades. She told me to send my transcripts to them today, and she would likely submit my application for reconsideration. However, she told me that all the spots at QM are pretty much filled by now, but to try anyways.
I have a feeling the case was the same for LSE, but I will not know that for sure now until I hear back from them via their undergraduate request form.
I feel much more relieved, because as I said, it was not the rejections that hurt (I am very used to rejections!), but it was the fact that it felt like my grades didn't mean anything. I do not actually expect to get into either university even if my application is reconsidered since these are highly competitive schools to begin with