Is there ANY other way besides surgery to flatten my protruding ears (permanently)?

Unfortunately non-surgical molding of the ear cartilages can only be done early in life before the cartilages get stiff and resilient. I am not aware of a reliable method to change cartilage folds in adults without surgery. 

Since you are in your twenties, your ear cartilage has fully developed, and a surgical approach may be the only feasible option for repositioning your ears closer to your head. Hope this helps! Dr Joseph

By the time you reach adulthood, the cartilage in your ears is no longer as pliable as it was in childhood. For this reason, it would be extremely difficult to “flatten” your ears without surgery. Surgery would be the most effective option. During your consultation, your surgeon will also be able to pinpoint what makes your ears look like they sit too far from your head, so that they can target that cause for a more effective outcome.

Changing the shape of your ears by non surgical ways is only possible in the first few months of life (new born to around 3 months). At this early age the ear cartilage is very soft and can be moulded using adjustable splints. Such splints work well for abnormal ear shapes and some types of protruding ears.
In older children and adults it is not possible to alter the shape of the ear by non surgical methods. There are a number of techniques available to set back the ears which are safe and reliable. These involve the use of stitches, the ear Fold or removing a small crescent of cartilage from the bowl of the ear. All can be performed under local anaesthetic (a general may be necessary in young children).
Not all protruding ears are the same and it is important to have an accurate assessment of your ears to find out what technique will give the best result for you.   I would always recommend you see a Surgeon who has an interest in this field and performs this surgery on a regular basis.

As infants, the ears are pliable, particularly during the first few days and weeks after birth. At this point, the ears can be shaped and held in place with splints or other devices to allow the shape of the ear to be altered. After the first few months of life, the success of this technique drops dramatically, and is definitely not an option in an adult.
Otoplasty is a surgical procedure to reshape the external ear to a more cosmetically-pleasing shape or position and has very high satisfaction rates. A consultation with a surgeon specializing in facial aesthetics can be very helpful to discuss the details of the procedure and answer any questions that arise.
All the best,