Hi Anne and welcome,
As already noted above, the more information/images you can provide, the better the information that can be provided in return. But here goes.
Your watch would be known as an open face pocket watch (or Lépine to the French/Swiss).
The case number you show (7444913) dates the watch (I guess) to about 1925/1926. The movement could be any one of several (similar) versions that Omega had been making for years.
The dust cover you show (first image) which is engraved with ‘Omega Bienne-Geneve’ and the medals – was typically used by Omega in this period. Bienne is the main city of Omega production but at that time watches were also produced in Geneva. The medals show the various exhibitions from previous years (Geneva 1896/Milan 1906/ Paris 1889/Bern 1914/Paris 1900/Milan 1906/Brussels 1897).
Your third image shows hallmarks on the inside of the dustcover. On the right is a Swiss hallmark (which is a grouse) above ‘0.800’ – which means the case is solid silver with a content of at least 80% silver. On the left of the Omega symbol is a German hallmark (crescent moon and crown) from this period. The other (scratch) marks have been made by watchmakers over the years.
In your fourth and fifth images we see the enamel dial – which has sadly but typically got cracks. That’s like a porcelain dish that has had some experience over the years – too bad. The lovely hands were (correctly) ‘Romaine’ hands (but sometimes loosely called ‘Cathedral’ hands).
Your watch is about 90 years old and has many stories (that it can’t tell you – make up your own). It may not have been serviced for 50 years (seriously) and although it may keep good time, if it hasn’t seen any oil for (a few) generations, it can’t be happy. Anyone would recommend that you try to find a watchmaker who doesn’t rob you but at least services the watch.
Finally, once it has been serviced, I’d recommend that you just enjoy the watch – pull it out of your bag while you’re in the supermarket queue and casually look at it (watch the queue around you!).
Good luck, Tom