I have a problem of playing consistently flat. I don't think my reeds are to blame since they crow at or slightly above a C; nonetheless, I always stick out as a little flat during band. My tone is fine, and blowing harder and faster still doesn't raise the pitch, so I think the problem is with my embouchure. When I press the reed with my upper lip, it raises the pitch, but the tone sounds kind of "hard," so I'm not sure what part of my embouchure I should adjust. Any help would be appreciated, thanks!
Sorry to hear of your problem. You don't tell me the make of oboe you are using and how new it is.
Sometimes these days as makers strive for a more mellow sound the oboes they produce have slightly thicker walls. This can lead to a slightly flat instrument. I know that from experience. You need to make your reeds shorter to compensate. What is not great is to bite up to raise the pitch as you say the tone hardens and you will also find that your lip tires very quickly and unfortunately bottom notes will not be affected by the pinching so the scale becomes uneven in pitch.
Nothing for it then really you to have reeds shorter. If you make your own try tying on to a shorter tube. Say a 45mm and keep the same length of cane. This will bring up the pitch as your reed will still be around a C or C sharp in its crow if it is balanced. Aim for about 68 to 69mm finished length.
I am pleased that you tell me the crow is around C at the moment because often flatness is caused by over scraping or by using a soft cane. Reed makers who make for young students always use a softer cane but make short reeds.
Keep your embouchure as relaxed as possible and let the breath do the work.
If you need a good reed maker who will make to your demands for a shorter tube And a slightly narrower shape (Gilbert -1) that also helps bring up the pitch try Roger Miller in Cincinnati. Find him on the web ROM Reeds. There are others but I have used Rogers reeds myself and they are well made.