There is nothing wrong in the first author or lead author being the corresponding author as well. In fact, for single author papers, that is always the case. The purpose of having a corresponding author is to facilitate ease of communication with the journal. Therefore, if you feel that it would be easier if you are the point of contact for the journal, you can go ahead and list yourself as both the lead author as well as the corresponding author. However, since your professor has made intellectual contributions to the study by laying out the initial plan and study design, he should definitely be a co-author. You can discuss this with your professor to ensure that there is no misunderstanding later.
- Corresponding author assigns co-authors without their knowledge: A case study
- Does your target journal allow more than one corresponding author? A case study
- What do the terms "lead author" and "co-author" mean?