If I contracted Lyme disease while on a school trip and brought bug spray that is helpful in preventing it but I was told not to bring it, do I have the right to sue?

I think it would be difficult to sue for contracting Lyme disease under any circumstances.  Bug spray and other measures are not full-proof.  There are other methods of preventing infection (such as proper clothing and looking for ticks after being in the woods or other outdoor areas), and noticing the bite in time to take very prompt action is important.  It would be very difficult to prove that you would not have contracted Lyme disease had you used bug spray.  Also, it sounds like you may have used bug spray (did you just bring it and not use it?).

I also suspect that your parents or guardians had to sign a waiver or release for you to go on a school trip.  Contracting Lyme disease is a risk whenever someone goes outside where the deer tick exists, which is pretty much everywhere in the United States.  It would be difficult to make the school responsible.