The most reliable way to establish whether your images are good enough for exhibition or publication is to seek the opinion of an independent expert. Appropriate people might be contacted through local photographic clubs. Alternatively, try for one of the widely recognized distinctions offered by organizations such as the Royal Photographic Society or British Institute of Professional Photographers. The assessments are excellent benchmarks against which work can be measured, and an invaluable source of constructive feedback. You may not like what you hear, but it is worth listening.
Another way to get your work noticed is to send about twenty of your best images to the editor of a magazine. A portfolio of this sort can be submitted electronically on a CD-ROM, or as prints or slides. Don't expect an immediate response. Editors are busy people and may hold your work for a few months if it is felt that it might suit a forthcoming issue. A further possibility is to enter photographic competitions offering worthwhile awards and prizes, and see how your work measures up against that of others.
The path chosen is a personal matter, and some photographers seek nothing more than the joy of creating images. Others have competitive spirit and pursue awards at club, regional, national or international level. A minority pursue publication through picture libraries, magazines, books and the Internet.