You're right. In this sentence, 'these days' means 'at the moment': you're probably referring to the current period of a few weeks or months, and you're talking about ongoing progress during this period. This period of improvement is temporary, and we presume that the weekly lesson is also temporary: you didn't take a weekly lesson before, and you might even stop taking weekly lessons as soon as you're fluent. So yes: the present continuous is a good tense to use here.