Without a canner you are limited to canning high-acid foods.
Botulism spores don't die at 212F, the boiling point of water. A pressure canner boiling water at 15PSI raises the boiling point to 250F or so which will kill the spores.
The bacterium cannot grow in a high acid environment and so high-acid foods such as fruit and pickles do not need to be processed in a pressure canner. Look for recipes for such foods. As use2199 said they will involve boiling the jars for a while to kill things.
An excellent resource is the Ball Blue Book that can often be found near the canning supplies in grocery stores. It always calls for Ball products of course but it has a ton of good canning recipes and instructions.
Don't experiment. Botulism is not a fun thing. Your lips get tingly and then you die shortly aftwards.
Pressure cookers and pressure canners are the same thing; with the canners being larger, and often having a pressure dial. Both can reach the same pressures and therefore temperatures if designed and manufactured correctly
The pressure canners dial gauge is more accurate for adjusting for food types and altitude, as you can get exact numbers not just 10 psi and 15 psi as with typical weight regulated pressure cookers. But for low acid foods you need 15 psi anyway
Pressure preserving is done because of the higher temperatures reached. This saves time and energy, and some food react better to a short 250°F (120°C) cook that an long 210°F (100°C) cook
Pressure preserving high acid food is worth doing as long as the food does not deteriorate quicker due to the high temperature (some soft fruits will)
For preserving low acid foods you need a known good pressure cooker that can reach 15 psi (103 Pa) and therefore 250°F (120°C)
With a commercially published recipe that has been acid level tested, you will have a published time that will be safe. For a home-made recipe you have to take the worst case scenario for the acid level of the main content, and cook for that. Your local government health department will most likely publish tables for this that you should be using. Remember to use altitude adjustments for timings too
Just relying on adding a teaspoon of vinegar or lemon juice per jar is not a safe and scientific method for raising the acid level, though many people do it, and have not come to any trouble with it?
You pressure cooker should come with a manual that confirms what it can or cannot do. Download a new copy if this has been lost
Also see What kinds of pressure cookers are there, and what are they good for?
Best Answer
In any food safety situation you really must ultimately ask yourself 3 questions to determine relative safety:
How High of a temperature am I sure I achieved?
How long did I hold this temperature?
How well sealed is the container?
If you are pressure canning, there are reasonably good chances you kept VERY high pressure and temperature. As for time, I cannot say.
For years my grandparents, my parents and myself have canned vegetables, soups, stocks, etc. and only rarely did we have errors because of some content of food. Most of our spoilage came from broken seals.
If you're confident in your canning technique, I see no reason why some egg white would hurt your stock. It's an animal protein just like any other.