You should get your blood pressure checked as well as your blood sugar level.
Normally broken vessels or subconjectival heamorrhage is not a serious condition. It happens and the blood gets cleared away after few days.
However, recurrent problem like your blood pocket might be an indication of
high bp or
diabetes. Therefore it is advisable to get checked.
Treatment
Use
cold water and wash your eyes frequently.
Dip cotton in chilled water and put it on your eyes for 2 mins. This process can be repeated multiple times. Use of rose water will have very good effects.
Put 2 drops of Ophthacare eye drops every night before going to sleep for a week, every alternate week.
If ayurvedic store is there in your city, buy
saptamrut lauha, take 250 mg tab/ powder in morning empty stomach 1/2 hour before breakfast, with warm milk.
Continue medicine for a month. Drop the next month and start again till the disease lasts.
Yoga for eyesight is a priceless and effective medicine for eyes. Please check online for eye yoga resources.
I also belong to the third world country.
Best wishes!