And I want to add too that celiac, especially in someone your age, can go into "remission" at times which means you could eat gluten a year from now & have absolutely no reaction at all --- but that does not mean that damage is not being done to a celiacs guts & the rest of the body.
There are a couple ways you could go with this if you want to find out if you are or are not celiac.
1) You can do a gluten challenge which means eating gluten for a specified time & get the blood work done & an endoscopy.
2)Or maybe you should talk to your parents about seeing your dad's doc who dx'd him. It might be that doc will consider your reactions to gluten along with your dad's dx & do an endoscopy on you to see if there is visible damage to your villi & dx you based on that.
Honestly, since your reactions are not all that bad yet it might be best for you to do the whole thing --- the gluten challenge, celiac blood panel, & endoscopy. Also, if you have siblings they should be tested.
As eatmeat said --- the rash & hives you get could be the early stages of dh which is the skin manifestation of celiac disease. This could also explain why you do not have such strong reactions b/c most of us with dh tend not to have many GI symptoms & even when we do they are not as severe. BUT that does not mean damage is not being done to our guts b/c it is!
Sage, we would welcome your friend as well as your dad if either should decide to join us here. We are always happy to help.