Another potential red flag might be that both degrees are from the same institution. However, this is something that can be surmounted.
For me, though, the major red flag is that you don't seem to have an advisor yet. This is a very important part of the process of getting a PhD.
So how do you set that up, you might be wondering?
You could start by reading about the different research areas represented by your department. Pick a couple that look intriguing, and read the faculty bios in that area. Once you have a short list of possible advisors, observe them at seminars, etc., perhaps take a class or sit in on some classes. Talk to other students. This part of the process might take on the order of a month.
Once you have a pretty good idea whom you would like to work with, it's time to read some of the papers that professor has written. It's okay if you don't understand everything yet. Start making a list of questions based on your reading.
Visit that person's published office hours, and ask for an appointment to discuss (name-of-paper).
When you get to that appointment (or in that pre-visit), mention briefly that you are a new PhD student and you don't have an advisor yet.
If the conversation goes well, ask if that person would mind giving you some advice about course selection. If the answer is yes, then send the professor an unofficial transcript by email, and any specific questions you may have about specific next courses.
Connecting with an advisor doesn't always happen exactly that way -- I tried to boil a complex, extremely varied process down to a simple procedure. You don't have to follow it precisely.
Happy advisor hunting!