Sorry, but I am not familiar with STDs. But as you and your friend did have blowjobs, it is likely that your spot may have been a bite, or a fungal infection.
If you look up syphilis on the web, it does mention about that in the second stage of the illness you could get a non-itchy skin rash appearing anywhere on the body, but commonly on the palms of the hands or soles of the feet, tiredness, headaches, swollen lymph glands. It doesn't mention that the rash comes and goes or whether it stays all the time.
And as you have experienced a rash that comes and goes on your hands and feet, it is better to get checked out as a precaution. It may just be that your rash is contact dermatitis like your doctor said, but as you did omit information to him, he would only be able to diagnose what he knew.
I do not think that you have syphilis. But I know this will be bugging you and preying on your mind until you get checked out and get the correct diagnosis. Find out if there is a sexual clinic that you go to get checked out. As I do not live in the US, I do not know what you have available.
Best wishes.
Is it likely though that I actually have a std from this? Especially a deadly one like syphilis?
You can find out the first, second and third stages of syphilis on the web.
If you are concerned, you could make an appointment and get checked out at a sex clinic. These are usually very discreet and no one would need to know where you were going. And you do not have to tell the clinic anything, but just go and get checked out.
I don't know if you have a GUM clinic in your local hospital or walk in centre. I am sure you would be able to find details about this.
It would be a good idea to get your scar checked out where you had your bump to put your mind at ease and give you the all clear.
Best wishes.