These are small bleeds, most probably happening when you remove or insert the contacts. Avoid contacts for a week, and use plain antibiotic eyedrop four times a day(moxiflox or ciplox) for both eyes,for one week, along with lubricating drops for both eyes
Next Steps
You can get an online consultation, to know in detail about the issue.
Health Tips
Gently insert and remove contacts, take care not to poke and injure.