Brief Answer:
Further evaluation needed

Detailed Answer:

Hello,

Well, the nose bleeding could be directly related to forceful nose blowing. Please avoid it, take some steam inhalation twice to thrice daily, it'll help as a decongestant and ease the sinus drainage.

Please drink a lot of fluids, don't blow the nose, if still bleeding anymore, keep pinching the nose gently by sitting upright. Do inform your doctor in case you're already on any blood thinners as the dosage needs to revised during this time.

Have plenty of warm liquids (soups, broth, porridge etc.), they'll act as an immunity booster and fasten the recovery.

Now coming to the blood clot inside the lower eyelid. As per your description, this could be due to subconjunctival hemorrhage (during forceful coughing, there can be increased intra-ocular pressure which in turn damages the small capillaries of the eye causing bleeding and such clots). Mostly, they're harmless and dissolve on their own within a few days only (around 7-10 days), provided there's no more forceful coughing / stress.

You can put on some artificial tear drops (eg. Refresh tears eye drop 1 drop in both eye three to four times daily) and observe how you stay.

If despite following this, there's no improvement within a while, or you notice the clots are increasing in size or any disturbances in vision, then please don't wait any longer and get yourself checked up by your physician / to the nearest ER (serial blood pressure monitoring, some investigations such as hemogram, coagulation profile analysis, a chest X-ray and Sputum microscopy with culture sensitivity should be done for further analysis).

As of now, just follow all these and monitor your progress, take rest. Let me know if I can assist you further.
Take care.
Regards

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