I have been in a similar situation.
One of my first jobs required me to actually pick up the phone and cold call people in different countries to sell my products. The first time I did it I felt just like you said.
But then something happened. I learned more about the product, and about the competition, and I actually started believing that we had something good. However that wasn't enough to get me excited about cold calling and reaching out to potential clients who were hundreds and thousands of miles away. Then I also realized that there is nothing wrong with trying to sell your product. Selling is as honorable as any other profession and there is no shame in it. But at the same time I also felt bad about interrupting people, however I also thought that they could always say no. And that train of thought worked more or less. The more I did it, the more comfortable I felt. Now I could cold call anyone in the world with total confidence.
However, selling your product doesn't necessarily involve cold calling. As a matter of fact, in most cases cold calling doesn't work. It is based on interruption, like the old marketing techniques.
Since you don't provide many details about your actual product, I can't actually recommend a specific action plan, but I think you need to get yourself in settings (trade fairs, chambers of commerce) where people are actually looking for suppliers and partners to IMPROVE their businesses and organizations. Don't see yourself as a seller, see yourself as a PARTNER. Naturally, this also involves pitching and talking to people, but face to face interaction is easier than over the phone.
You have actually accomplished a lot. You have developed a product that seems to be pretty good (you said that people actually find you, not the other way around), and only for that you have my utmost respect. Now you need to push a little bit more, and spread the word about your product: use trade associations, trade fairs, blogs, and be proud of what you have.
Some of my friends are trying to sell some app that they have developed for high schools but they are not pitching the product directly to high schools. They are actually meeting with state education officials and trying to persuade them to buy the product at state level. Maybe you could also consider that route.
Finally, one last piece of advice. Show confidence. Never hesitate or doubt in front of a potential client. But don't overdo it either. Selling is like trying to find a wife, or husband, it pays to look interested, but not desperate.