They're called "allergic shiners" or "allergic facies" and are believed to be caused by increased blood flow and general congestion in the sinuses that cause some pooling of blood in that area.
They can be very hard to get rid of.
Unfortunately, you probably have to deal with the underlying sinus and allergy issues to get rid of them. That means you should be doing the following:
1. Taking an antihistamine daily (Zyrtec is probably the best option because it's over-the-counter and very effective).
2. Use a neti pot or SinusRinse bottle to irrigate your sinuses 2-3 times a day.
3. I assume the nose spray your doctor gave you was a steroid nasal spray - use that as directed. If it wasn't a steroid nasal spray, you should ask your doctor for one and use it daily.
4. Take 12-hour Sudafed in the morning if you feel congested.
5. If you have any symptoms of acid reflux (occasional heartburn, etc.) ask your doctor if it could be effecting your symptoms. Acid reflux has been identified as a cause or complicating factor in many people's sinus symptoms, and it doesn't respond to allergy treatment.
6. Allergy shots are an option you should check in to but they take many months to deliver results.
All of this stuff takes time so you'll have to be patient. It may take 2-3 months before you notice a significant improvement.
Dark Circles Under Eyes, WHAT TO DO??? 
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