Does what I feel of regurgitation or saliva, which I then swallow, count as breaking my fast, given my doubt about its nature, and do I have to make up for it?

Fasting is only invalidated by certainty of the occurrence of that which spoils it, and doubt does not invalidate it. So, as long as you are not certain that you swallowed the phlegm after it reached your mouth, your fast is valid, and you are not required to make it up. You should ignore obsessive thoughts.