Great question OP! I have a PhD in this topic.

TLDR:

• Drugs such as chemotherapeutic agents that damage the nervous system can enhance pain
• The term to describe this enhancement is hyperalgesia
• The processes that cause it are peripheral sensitisation and central sensitisation
• LTP, or an increase in ion-channel expression at the neuronal synapse, is one of the many mechanisms involved
• In the case of LTP, the main neurotransmitter is glutamate

Analgesics are drugs that work by reducing pain, and the opposite of this would be drugs that increase pain. The term used to describe an increased pain response is hyperalgesia.

An example of a condition that can lead to increased pain is chemotherapy-induced peripheral neuropathy (CIPN), which is caused by chemotherapeutic agents that damage the nervous system. This damage can result in peripheral sensitisation, through hyperalgesia and ectopic firing. Peripheral sensitisation occurs when the threshold for activation of high-threshold pain receptors is lowered, and their responsiveness is enhanced (hyperexcitability) when they are exposed to inflammatory mediators and damaged tissues. This can lead to central sensitisation as well, but that's a more complicated process [1].

Long-term potentiation (LTP) is one mechanism that can lead to sensitisation through increasing ion channel expression at the synapse. It occurs when the connection between neurons is strengthened due to increased firing frequency between them. Some studies have shown that ketamine, which is an NMDA antagonist that inhibits LTP, can have analgesic effects in cases of peripheral sensitisation [2]. This shows that LTP is one of the mechanisms involved in sensitisation.

P.S.

There are also surgical methods to enhance the pain response which we do in research to model disease. One example is chronic constriction of the infraorbital nerve (CCI-ION) to model trigeminal neuralgia.