Brief Answer:
yes

Detailed Answer:
Hello and thank you for your question.
It is not unusual to have some disruption of small blood vessels if you are coughing a lot. However, if you are having fevers or have been expose to anyone with tuberculosis then you should see a doctor as soon as possible.
Residual coughs after a cold can last for weeks. Use cough drops and cough syrups to ease the coughing. Stay well hydrated and take some extra vitamin C.
I hope you feel better soon and let me know if you have further questions.
If the coughing up blood does not resolve soon, see a doctor.
Regards,
Dr. Robinson

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