Correcting yourself in mid-sentence is not only grammatically and contextually fine, it is one of the classical rhetorical figures, called metanoia.
In his book Classical English Rhetoric, Ward Farnsworth defines it thus:
Metanoia (met-a-noi-a) means correcting onself; the speaker is, to take the old Greek name of the device literally, changing his mind about whatever has just been said. Of course it might seem more efficient to just say the thing right the first time, but metanoia can have attractive rhetorical consequences.
a. To stop and correct oneself usually is unexpected; it slightly disrupts the flow of a piece of writing or speech. The disruption attracts attention and gives emphasis to the revised claim.
b. The device allows the speaker to say something and then take it back, thus avoiding some responsibility for the utterance while still leaving it to linger with the listener; retracting a statement does not entirely erase the experience of hearing it.
c. Metanoia can have a mild persuasive value. The speaker may utter a less controversial claim, then revise it to make it stronger. This brings the reader along more gently than announcing the stronger claim on its own. Or conversely the stronger claim may be offered first but then reduced to something less ambitious that seems easy to accept by comparison.
d. Metanoia, like an aposiopesis, often creates the impression that the speaker is working out his words — that he is thinking, not just repeating something already thought out and polished. Sometimes the device more specifically suggests a conflict within the speaker. Different views or impulses audibly struggle for mastery.
e. Metanoia can create an impression of scrupulousness, as the speaker starts to say one thing but then feels obliged to take the initiative in correcting it. (It also can suggest overscrupulousness, as when the speaker fusses too much.)