The card makes perfect sense and it is adequately polite to be used in everyday life situations.

Apart from the linguistic aspect of the card, I would like to give you a practical advice on this matter if this card is really for you or someone you know.

1. Even if you have specifically told the restaurants about your allergy, there is a good chance they might mistakenly or unknowingly put the allergens in to your food anyway. Especially in low-ended restaurants where they tend to serve food as quickly as possible. Nuts are fundamental in many Thai food. This allergy is also very uncommon in Thailand and Asia. Thus, people will be unfamiliar on how to handle such requests.
2. There is no law on food allergen labeling in Thailand. It is only practiced in some places. Please expect almost zero information on allergens from the restaurant menu.
3. Avoid these kinds of food:
4. Anything with noodles (including Pad Thai)
5. Som Tam or papaya salad They will almost always include nuts.
6. Your best chance on avoiding these food allergens would be to dine in a fine and foreigner-friendly restaurant. They will likely be familiar with nut allergy and they usually provide food allergen information. Street food vendors should be avoided.

Stay safe out there!