Is it possible to determine if fish caught from fishing is safe to make into sashimi or sushi?
The biggest concern with fish caught in the wild is the presence of parasites. You'll have to look up which species of parasite are present in the species of fish that you wish to use, and treat it accordingly. Tapeworm is common in salmon, and several other varieties of fish have various parasites capable of infecting a human host. Most sites I've seen suggest that you need to freeze the fish at -4 degrees Fahrenheit (-20 Celcius) or colder for 7 days or -31 Fahrenheit (-35 Celcius) for 15 hours to guarantee any parasites are dead. Many home freezers may have difficulty keeping temperatures this low. Also the freezing process, if done in a home freezer, has a good chance of ruining the taste and the texture of the meat. You may want to look into flash freezing methods to avoid this.

Supposedly there are certain species of fish that do not have any parasites, or at least no parasites capable of infecting humans. You will want to do your own research on this to be certain.

Beyond parasites bacteria are the other biggest concern. Make sure you put the fish into a cooler immediately, and freeze it as soon as you return home.

Sources:
http://seafoodhealthfacts.org/seafood_safety/patients/parasites.php
http://www.sushiencyclopedia.com/sushi_concerns/sushi_parasites.html