I think you are right in your assessment. Red blood is fresh and probably from straining. There are some stool softeners you can buy in the pharmacy/drug store that don't required a prescription and are not expensive. It will help soften the stool so it can be passed more easily and without straining; the hemorrhoid can then heal. I take one stool softener two times a day.
Here is a link to more information:
http://www.mayoclinic.com/health/hem...CTION=symptoms
Sometimes a visit to the doctor is reassuring and gives peace of mind...