Was it Dell or was it a scam?

I received several phone calls yesterday morning, from someone saying they were a Dell tech from Dell Customer Service. I did not answer these calls at first, because I thought there was no reason for Dell to be calling me, other than telemarketing sales, which I do not accept. However, when the calls became annoying, I picked up, and was told at that time that Dell was receiving messages from my laptop that it had been downloading malicious malware for a couple of weeks, and that they had sent me several notification emails that this malware would be extremely detrimental to my computer.  Now, I thought scam right away, since I have had viruses and malware in the past, yet never received any warning calls from Dell. Plus, if I ever thought that Dell was tracking info on my PC, I would be furious! This call would have ended right then, except this woman asked for me by name, she had my phone number, she knew the model of my laptop, and, when she phoned me, my caller ID said, "DELL"  1-800-624-9897. That is the number that is listed for Dell Customer Service, as I looked it up while she spoke. And although most of what she was saying seemed a little off to me, I was pretty side tracked by her personal knowledge of my private information, and typed in the information she gave me, in the command box, which brought up a page full of errors and warnings, which she said I never got as they must have been blocked by the malware, and she asked me to go to my downloads and see what was downloading. When I got there, nothing was downloading, but ShowmyPC.exe, which I had never heard of,  was there waiting. I assumed this application was the virus, which I certainly never downloaded, but as it turned out, that it was her application, allowing her to come into my PC and take control. How she got it on my laptop, I do not know. Her Indian accent was so thick, I could barely understand her, and I just felt uneasy about the entire call, so I terminated the session, saying I would have to call her back when I had time to deal with the situation, and hung up. After that, I received two more calls that evening, and have gotten 3 more calls this morning, all saying Dell, on the caller ID, and all from the same number I gave above. I didn't answer. Although I had ended the call before I was asked to pay anything for a fix, I knew it was leading up to this, and put it all down to a scam! My concern now, did this woman implant malware in my laptop when she had control of my computer? Or, were these calls actually from Dell? Does Dell do that? I received my first error message this evening, error 3048,3. I had to download NPE and do a rootkit scan.  There was a problem in my registry, which it was able to fix. But, is this thing finished with me? I have many concerns about this,  but mostly, how did these people get my personal info from Dell?  Had they not been able to provide it, I would have never, never, allowed them into my PC, and wouldn't be second guessing if the call was legit or not, at this point. Does Dell receive transmitted information from the PC's I buy from them? And if this woman was saying this based on the concierge program that I once had, that thing was on another PC, and had been uninstalled in 2013. But, that would tell me that the people who are doing this, if it is a scam, are either employees or ex-employees of Dell, who are stealing, or who have stolen customer information. I will sell all 6 of my Dell computers and the Dell printer too, and never buy another, if this is true. Who can I call to find out if the calls I received were really from Dell?