I think your film was processed by hand or semi-automated equipment in a small lab. These appear to be squeegee marks from your description of them.
Automated equipment produces consistent and parallel results. You describe inconsistent and irregular results. Inconsistencies usually happen as the result of irregular, unusual, or careless manual processing.
At the end of the processing, film is usually hung up to dry in a drying cabinet if not by forced air in a fully automated film processor.
These marks are consistent with a manual means of removing extra water from the strip of film after the final rinse to shorten drying time.
Various means are used to do this. The two most popular ways are with a very soft chamois "cloth" (It's really leather) or a hand-held windshield wiper like device. If either thing is contaminated, it will scratch the film.
Now, the question remains as to what you can do to remedy the problem, if anything.
If the marks are on the very shiny side, they may be either scratches or water marks that have dried on the base of the film. If they are water marks, the film can be re-washed and re-dried or cleaned carefully with film cleaner on a wad of cotton. If they are scratches, they can be minimized with anti-scratch solution next time you get prints. Ask for custom printing.
If the marks are on the dull side, there's little you can do to save the pictures short of having them retouched to remove the imperfections if they're important enough.