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Sunscreens contain several different components. These make them effective at absorbing UV, pleasantly-fragranced and give them a shelf-life. Most people will not react to these at all, but if you are unlucky you might develop a specific allergic reaction to one of these chemicals that produces red, itchy or uncomfortable reaction like eczema called a contact allergic dermatitis. Sometimes it might even blister.
You can become allergic to something you have used without any problems for years, but once you have become allergic, it is likely that you will be so from that point onwards. Sometimes it is not the chemical itself causing the problem, but a combination of the chemical and sunlight, causing a photocontact dermatitis.
If you do have problems with reactions to sunscreens switch to a different brand or it look for sunscreens designed for sensitive skin which contain mostly physical blocking agents like titanium dioxide and less chemical sunblock molecules. Examples include Sunsense Sensitive, P20 and Actinica.
If you are sensitive then test the sunblock by using it on a small patch of skin on your forearm for a few days. If you develop a rash at the site of application then avoid that product completely. The most accurate way of assessing for possible allergy is to have patch testing done by a dermatologists specialising in this. This should tell you exactly which component you are allergic to, and enable you to select a sunblock without this chemical.