i think the "string" and blood clots are 2 different issues and am a little confused as to why your vet said that, but he is a vet, and saw your animal; i am just commenting on my understanding and i could be wrong. blood clots that cause them to swell in excess and for an excessive length of time are the result of continual hemorraging (sp) and the string is something left in there that will cause infection.
all of them are going to bleed some, but on occasion one will continue to bleed and once the sac seals off it will swell and sometimes a lot. i have only seen one in my life and he swelled so bad that he limped from it and his side was swollen. the vet said that most likely it was an infection from the string. and that is very logical. in this case however it was not. it was clotted blood. 2 or 3 cups of jellied looking blood were mashed out when he was opened up. he had to be opened a few more times and each time less and less came out. this went on for about 2 weeks i think. once you open them up they will seal fast, so if you can spook them and make them bolt off it will cause the sac to open on its own and drain, but you have to do this about every hour after they are opened because it wont take long for the sac to seal off. this was done to that calf 2 or 3 times after he was opened each time to drain more off. he finally got over it.
if it is an infection from the string i think after a week and a half the vet would not have had to suspect it. i figure that pus would have definitely been visable. and if it is the string, you will have to have it all dug out so to speak.
good luck
jt