A true allergic reaction can take up to few days to show itself in the form of dry, itchy, inflamed skin, as opposed to the stinging sensation which is immediate.
If you are exhibiting allergic reactions to fragrance oils, stop using them or try different ones. You could be reacting to a number of different components in the oils, and it's hard to tell which ones cause the reaction. The main culprits in fragance oil allergies are cinnamic alcohols and aldehydes, citronellol, geranol, and linalool, most of which are generated from essential oils (which means switching to an essential oil won't help...). Where do we find these culprits? In cinnamon, aniseed, star anise, nutmeg, clove, vanilla, bay leaf, parsley, ginger, paprika, pepper, cumin, and coriander, to name a few. If you can handle essential oils but not fragrance oils, then it is very likely that fragrance is not the culprit. (Remember, I'm not a doctor and these are not diagnoses, just thoughts...)
If you are exhibiting allergic reactions to preservatives, the main culprit is likely to be one of these five things - Diazolidinyl Urea (liquid Germall Plus and Germaben II), Imidazolidinyl urea (DMDM hydantoin), Bronopol (not sure which one contains this, but it's nothing on my preservative page), or quaternium-15 (again, I haven't used one of these). You'll to have find another preservative that works for you - interestingly enough, allergic reactions to parabens are quite rare, so those are a good option.
There are other things to which you can be allergic - anything with proteins, aloe vera, butters, and so on - but that is far beyond the purview of this post. So I'm not going to suggest any possible ingredients for people with an allergic skin type because you're better off visiting a doctor or dermatologist for patch or skin types. If you do have this skin type, figuring out exactly what is bothering you won't be easy and formulating might be a little difficult, but it's worth it because you shouldn't be in agony!