Welcome to JA and thanks for asking
Bleeding from penis can be due to infection. If the bleeding is coming from the urethra while passing urine than it can have many reasons. It can be due to a urinary infection,calculi,prostate infection,trauma,bleeding disorders,some diseases of the urinary bladder and even kidneys.If this is a new development i would suggest to see your doctor for examination to find out where exactly is the problem and then he can guide you further investigations accordingly.If the bleeding is continuous i would suggest an evaluation in urgent care.
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If it is coming from the same area where the abscess is then its quite possible that it could be due to the abscess but if it is coming from a new site then other possibilities as i mentioned need to be considered.
Yes if it is a continuous bleeding i would suggest to have an examination
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