My dog is in season and she is bleeding very heavily. I took her to the vets yesterday and the vet said that everything is fine but I think the bleeding is not normal. She is 10 years old and she has been spayed by a different vets, however tests showed that she is in season. Would it damage the dog if I bought antibiotics and gave them to her?
Antibiotics are not likely to be the answer here. If your dog has been spayed properly, it will not come into season at all. Therefore something is not right here. A "heavy" season in an older dog can be due to a uterine problem and might need surgery to treat it. If your dog is at all "off colour", vomiting at all, getting extra thirsty or urinating lots, or the blood looks dark brown/red and is thick rather than watery, you need to go back to your vets to get her checked out again.
If she is bright and well and just having a season, then it will probably pass, but she clearly has not been spayed properly.
Not something we can help with really; your vet's are in the best position to do this.