Hello. Thank you for coming to JustAnswer with your question, and welcome.
Your symptoms suggest that you may have some gastric reflux causing irritation in your esophagus and/or throat. Gastric reflux can also affect the mucous membranes higher in the back of the throat, and the sinuses, which could cause some blood tinged mucous. It can also lead to sinus infections.
You may want to ask your doctor about these symptoms. You may need a change in the dosage of the omeprazole, or a change of medication to something stronger.
Other things you can do yourself to help with gastric reflux, if this is what is causing your symptoms:
Do not eat for 2 - 3 hours before you go to bed at night.
Avoid foods that can exacerbate your symptoms, such as citrus, tomatos, peppermint and caffeinated or alcoholic beverages, to name a few.
Eat smaller more frequent meals as opposed to 2 or 3 large meals.
Avoid high fat, or fried foods.