I used to have only a few students, but am these days far busier. Indeed, six have come to me in just three days. A little overwhelmed at first, I have gradually adjusted to the bustle. At the same time, worries over the quality of my teaching do trouble me a bit. Pushing those worries aside, I will do my best to handle my new increased workload.
I have rewritten your sentences so that none but the first begins with "I", and "I" is used three times instead of six. As a matter of style, it is preferable not to start many sentences and clauses with "I". ALL of your sentences and clauses start, or almost start, with "I". Persistent use of "I" as a subject makes your writing appear to be self-centered. The suggestions I have made are intended to show you some ways to avoid creating this effect.