He could have had the parasites before you got him, or he could have gotten them from the bloodworms. Freeze dried blood worms are not very good for Betta fish because the freeze drying process takes out most of the nutrients, and you end up with basically candy for fish. If he won't eat the other things, you're going to have to fast him until he will. Don't worry, Betta fish can go many, many weeks without food. I would fast him for a few days, and see if the stringiness goes away (it could be he's not digesting the bloodworms properly). You can use epsom salts to see if that will draw the parasite out, if it's a parasite, until you get medicine.
But please stop feeding him the freeze-dried bloodworms as his primary food, he will be much healthier and live longer in the long run. Once he is hungry enough, he will eat the pellets.