I would probably follow roughly the following steps:
Read the conference paper thoroughly, and decide how it relates to your paper. This part is regardless of the details of who published first; it is just a matter of knowing the facts, and clearly figuring out what their work is about, how it overlaps with yours, and to what extent the results are the same or different.
For results that overlap significantly, determine who published first. You state in your post that you have been working "since mid-2017" and "my research started earlier". To be clear, those details are not really relevant here. The only thing that is relevant is who published first. Fortunately, you are hopefully OK here as it sounds like you have publications in this topic as well.
If the authors of the conference paper could have cited you, but didn't, consider reaching out to them directly. From your post it sounds like they didn't cite you, even though you had already published? In this case, you can send a polite email saying you saw their work, it looked interesting, and asking them if they are aware of your earlier work. You should assume good faith; it is likely that you both completed similar work in parallel.
Write a section on the paper in your related work (to your thesis), explaining how the research differs. How much you say mainly depends on how related the work is, not when it was published. If it happens that the works have some of the same ideas and solutions, you can explain this in a number of ways, depending on the results of (1), (2), and (3):
"[X et al, 2019] also developed a similar solution in parallel to our work."
"[X et al, 2019] have a different idea on how to solve problem P, based on QRST, however, they did not compare with [your name et al, 2018]."
"Some aspects of our solution, including ___, were originally developed in [X et al, 2019]."
While the above are useful phrases to cover yourself from criticism, these should not be the only thing you write, and you should only say these as a last resort. It is much better if the work differs in some way, and you can explain clearly how it differs. Even if only part of it differs, explaining which parts differ will be much more helpful to future readers.
Some other comments:
So far, I did not cite my own papers in my own thesis (this is what my professor told me).
This is really strange to me. If I were reading your thesis, I would really want to know what papers of yours you are building on. But the culture may be different between my field and yours (I am in Computer Science). Your advisor of course knows best.
Now, it is not clear when I started doing my research.
As I said above, this isn't super relevant; it's more important who published first, and whether the work was done in parallel.
And of course, I would like my research to be considered novel in the thesis.
We all would like this :) This is the best reason to have a thorough comparison, so you know how your work differs, in case anyone asks. If it doesn't differ at all, but you did the work in parallel, that may be fine as well. And if you published certain results first, don't be afraid to highlight that in your thesis or if anyone asks you about it.