I have been working on designs for quite a while and usually used some open fonts or purchased some for the creatives. But I was wondering if I can design my own font in photoshop, then it will be feasible to create the structured font as per the design.
You can design glyphs (=the letter shapes) in any drawing media, Photoshop is not different in that sense. Also experimenting and deciding how the glyphs should be placed to make writings is possible in any media. But generating computer font (=software) such as Arial.otf or Courier.ttf with glyphs and all placement rules needs a font editor. Many of them want the shapes as vector drawings, so Photoshop isn't at all good for them. They have some minimalistic drawing tools included, but as well one can import vector shapes.
One simple solution is to place your glyphs to Scanahand input form. That software generates a font from bitmap images. It's intended to handdrawn letters, but nothing prevents to fill the form in Photoshop.
Scanahand makes vector based fonts, it traces the bitmaps.
Search for bitmap font editors if you want to generate bitmap fonts. They can be today fine like vector fonts, (=far from crude dot matrix printer fonts) and even colored, because today their memory requirements are nothing special. Vector shape based font software became common in the era when few megabytes of memory was considered as pretty much.
Photoshop and Illustrator have a commercial font generating extension named Fontself.