"However, the fact that I am here right now having thoughts means that their existence is necessarily true."
Employing your statement as an axiom concerning human thoughts/ideas, we can then introduce Spinoza's Proposition 43 from Ethics Part 2, On the Nature and Origin of the Mind, as a corollary to your axion;
"He, who has a true idea, simultaneously knows that he has a true idea, and cannot doubt the truth of the thing perceived."
Explanation- No matter what differing skeptical schools of philosophy may say about doubts concerning human knowledge, your 'axiom' concerning the necessary existence of thoughts, coupled with Spinoza's proposition and his Note which will follow below, should help anyone to see, that if you know that your mind entertains adequate ideas, then please do not let anyone else convince you otherwise!
Note.— "I explained in the note to II. xxi. what is meant by the idea of an idea ; but we may remark that the foregoing proposition is in itself sufficiently plain. No one, who has a true idea, is ignorant that a true idea involves the highest certainty. For to have a true idea is only another expression for knowing a thing perfectly, or as well as possible. No one, indeed, can doubt of this, unless he thinks that an idea is something lifeless, like a picture on a panel, and not a mode of thinking—namely, the very act of understanding. And who, I ask, can know that he understands anything, unless he do first understand it? In other words, who can know that he is sure of a thing, unless he be first sure of that thing? Further, what can there be more clear, and more certain, than a true idea as a standard of truth? Even as light displays both itself and darkness, so is truth a standard both of itself and of falsity."
It is high time for each of us to move on from the self-negating philosophies which began with Descartes and his impossible claim to actually doubt those things that he truly knew.