Employment Law Questions? Ask an Employment Lawyer.
There are no laws that protect you based on the facts you have presented. Since your employer has a written policy that employees share a room when they travel you are required to abide by the employer's policy. If you want an exemption from that policy they may require you to disclose this reason and if it is medical there is no law that stops them from requiring you to disclose or forcing you to share if you will not disclose. You assume that your roommate would be aware of your condition if you shared but that is not a known fact so by forcing you to share there is no conclusion that this will force you to disclose because your roommate will be aware.
I could not find any case law that stated herpes is a disability covered by the ADA. But you could make that argument but to ask for a reasonable accommodation for a paid individual room you would have to disclose your disability to your employer.