This is getting too long for a comment:
When you say 'in its place', are you looking for something to sprinkle on finished food, or do you have a specific recipe in mind?
True 'peppercorns' (Piper nigrum) are from vines in the Piperaceae family and get their heat from piperine. This includes white, black & green peppercorns.
You might try things from other botanical families, but without knowing exactly what causes your reaction, I'd recommend using allergy testing techniques from survival guides before using it in your food.
Other things sold as 'pepper' include:
Pink peppercorns (Schinus molle) are in the Anacardiaceae family (which includes cashews, pistachios, sumac and poison ivy). They may cause a reaction in people with nut allergies). They have a peppery note, but with a floral quality to it.
Be warned that Brazilian pepper (aka baies roses de Bourbon; aka Christmas Berry, aka Red peppercorn (variety terebinthifolius), aka Florida holly; Schinus terebinthifolius, family Anacardiaceae) can also be sold as 'pink peppercorns' (variety acutifolius), but had previously been banned in the US (still is in Florida) as it's both an invasive species in many areas can cause poison-ivy like reactions if you touch the sap, and the berries are believed to cause vomiting and other adverse effects in some people if ingested. The US FDA does not designated it 'GRAS' (Generally Regarded As Safe).
Sichuan (Szechuan) pepper (aka. Chinese pepper; typically Zanthoxylum bungeanum, but could be anything in Zanthoxylum, including Japanese pepper (sanshō; Z. piperitum), Korean sansho (Z. schinifolium), Wild peppercorn (Z. simulans), etc.). It isn't 'peppery', but it's citrusy and causes your lips and tongue to go numb in larger amounts.
Crushed Red Pepper are dried and crushed chili peppers (capsicums), which get their heat from capsaicin. Although most people are familiar with the stuff at pizzerias, it can be made with other varieties of chilis with more interesting flavor profiles, such as Aleppo pepper
You can also consider some ground capsicums like hot paprika, or specific ground chilies (jalapeño powder)
Alligator pepper (aka. Grains of Paradise) See Jefromi's answer. It's peppery with an interesting background to it. (some folks say citrus & cloves)
Not sold as 'pepper', but another sice to sprinkle onto food to wake it up:
