From Victoria Groce,
Your Guide to Food Allergies.
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A.

Yes. None of these seeds are tree nuts and, in fact, they are all commonly used in cooking as substitutes for tree nuts and peanuts because they provide a lot of nutritional value and are somewhat similar in taste.

Both sunflower and pumpkin are rare allergens, with few cases reported worldwide. However, do be aware that sesame seeds are considered potent allergens. Sesame allergy is among the more common allergies in countries such as Israel and Australia where consumption of sesame-containing foods (like tahini paste) is high, and it's considered one of the nine major allergens by the Canadian Food Inspection Agency. Your allergist is the best source for advice on whether sesame seeds are an appropriate part of a diet for a child who has been diagnosed with other food allergies.

Sources:

Gangur, Venu, et al. "Sesame Allergy: A Growing Food Allergy of Global Proportions?" Annals of Allergy, Asthma & Immunology. Jul. 2005. 95(1): 4-11(8). 4 Jan. 2008.

Hsu, Denise C. & Constance H. Katelaris. "Is 'Nut-Free' Sunflower Butter Safe for Children with Peanut Allergy?" Medical Journal of Australia. Nov. 5, 2007. 187(9): 542-43. 4 Jan. 2008.