This is a good question. As it is difficult to know what the cause of your rash is without seeing it, it is very important that you make an appointment with your primary care doctor
to have a full history and physical examination. If it is over the weekend or you can't get an appointment with your doctor, you may want to consider going to an urgent care facility. Dogs carry thousands of bacteria on their feet so I am concerned for infection since your bumps and rash are at the site of the scratches are. This would more likely be the case if the area is warm and the bumps are red. If this is the case and you have any swelling of your arm or fever
it is urgent that you seek care immediately as you might have cellulitis, which is an infection of the skin that is untreated can be very serious. The other possibility is that you have contact dermatitis, which is irritation of the skin from something it came in contact with, in this case, your dogs nails. Again, it is very important that you seek care to obtain a correct diagnosis and get appropriate treatment.