**Core Concept**
A sexually transmitted infection (STI) caused by a viral agent, leading to genital ulcers and lesions in an HIV-positive individual.

**Why the Correct Answer is Right**
The clinical presentation of small painless nodules that burst and become open, fleshy, oozing lesions, is characteristic of primary genital herpes infection. This is caused by the herpes simplex virus type 2 (HSV-2), but can also be caused by herpes simplex virus type 1 (HSV-1). The presence of HIV co-infection increases the susceptibility to opportunistic infections, including HSV. The lesions typically progress to form beefy red ulcers, which are a classic sign of genital herpes.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because syphilis typically presents with a single chancre, which is a painless ulcer, but it is usually solitary and not associated with the described lesions.

**Option B:** This option is incorrect because charcoal is a painful genital ulcer that occurs due to Haemophilus ducreyi infection, but the ulcers are typically multiple and painful, not painless.

**Option C:** This option is incorrect because lymphogranuloma venereum (LGV) is an STI caused by Chlamydia trachomatis serovars L1-L3, which presents with a painless papule or pustule, followed by lymphadenopathy and bubo formation, not the described lesions.

**Clinical Pearl / High-Yield Fact**
Genital herpes can be diagnosed clinically, but laboratory confirmation is often required. A rapid antigen detection test or PCR can be performed on lesion swabs to confirm the diagnosis.

**Correct Answer:** C.