Brief Answer:
As discussed in details below.

Detailed Answer:
Hi.
Thanks for your query.
To recapitulate: Female/36 - stomach pains that felt like hunger for the past few days - hard lump under sternum - tender - causes hunger pain like pressure - was on Z-pack last week - pain started around then...

As per the history you have provided, the lump below the sternum may be diffuse lipoma, or an epigastric hernia with trapped fat causing tenderness.
Pressure on that is transmitted to the stomach hence causing the hunger like pains - Z-pack and many more medicines are known to cause or enhance gastritis.

I would advise you the following:
Get a high resolution ultrasound of the abdominal wall at the are below sternum and of the whole abdomen.
Take a PPI like Omeprazole, antacid and see if the hunger pains reduce or not.
Soft bland diet, frequent small meals made at home.
No oily spicy foods.
Warm liquids only.
Avoid the foods and beverages that can instigate or enhance the problems.

Consult a Doctor for clinical evaluation, examination and if required a reference to the General Surgeon and Gastroenterologist.

I hope this answer helps you, please feel free to ask for further relevant queris if you feel that there is a gap of communication .

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Brief Answer:
Let us find the original cause.

Detailed Answer:
Why to think of something so rare and dreaded, like lymphoma?
Yes, the blood tests can indicate for further evaluation for many diseases like lymphoma.
I hope your Doctor has not suggested anything like this.
Please get all the clinical evaluation and investigations I have suggested above to get the correct diagnosis so that you will be treated accordingly.
Medical field depends upon the facts hence the necessity to have fresh clinical evaluation as there is pain and tenderness.
Please give feedback once all the things are done.

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