At first glance, you have several issues here:
1. This is an issue of trademarks, not copyrights. (Note that I use trademark and logo interchangeably)
2. The "clip art" containing the FAMU's Rattler head logo is FAMU's trademark which they own. You did not have a right to use FAMU's trademark. This is no different than FSU's Seminole head or UF's Gator head -- you can't take those and use them either.
3. You should have had a written agreement with the printing company stating that you are providing them with your original logo, and you give them a limited license to print the logo only on shirt/uniforms that you order for your organization. The printing company may have infringed your team's trademark by printing your logo on other shirts (shirts for another customer).
4. The competing team, now using the identical logo, may also be infringing as they have subsequently adopted a confusingly similar trademark.
5. Unregistered trademarks are protected at common law. The first user/creater of the logo can force another to stop using the same/similar logo. However, this would involve legal action. Additionally, you would have to prove your team's rights to the logo, which as stated above, may cause problems because you do not have permission to use FAMU's Rattler logo as a portion of your logo.
6. If you did have any kind of suitable agreement with the printing company, such an agreement would probably guarantee to them that the logo is your original and does not infringe on anyone else's rights, and if it does, you will indemnify them for the damages. Again, you did not have permission to give the printer the right to print the FAMU Rattler, and FAMU could just as easily sue the printer and/or you and/or you would have to indemnify the printer for infringement damages to FAMU.
So, the point here is that you may open up a whole "can of worms" if you try to go after the printer due to the use of the FAMU Rattler logo. A better option may be to contact the other team and ask them to change their logo -- which they may not be willing to do due to expense of buying all new shirts/uniforms.
If you wish to pursue the matter, you should retain an attorney to evaluate each of these issues and others, to propose a suitable course of action (to minimize your risk and expense), and to handle the matter for you.
Best of luck.