He notado hinchazón en mi muñeca.

In Spanish, he notado is the present perfect (haber + past participle) and implies a connection to the present: “I have noticed.” Noté is the simple past (pretérito) and refers to a completed action: “I noticed.” In many parts of Spain you’d typically hear the perfect for very recent events, while in Latin America both are common:
• He notado hinchazón → emphasizes that the swelling is still relevant now
• Noté hinchazón → simply states that you noticed swelling at a past moment

Spanish often omits the definite article when naming symptoms or general conditions—similar to “have fever” in English (though English still uses an article). Compare:
• Tengo fiebre (not “tengo la fiebre”)
• Siento dolor de cabeza (not “el dolor de cabeza”)
So He notado hinchazón en mi muñeca treats swelling as a general symptom. You could say He notado la hinchazón only if you’re referring back to a specific swelling already mentioned.

• Hinchazón = swelling, the visible puffiness or enlargement of a body part.
• Inflamación = inflammation, the medical/biological process often involving redness, heat and pain.
Use hinchazón when you simply describe puffiness; use inflamación when you want to stress the clinical aspect or internal process.

The preposition en indicates location (“in/at”), which you need to say where the swelling is. A would indicate movement toward (“to”), e.g. Voy a tu casa. When describing symptoms or states, always use en:
• Tengo un moretón en la pierna
• Siento picazón en el brazo

You can add ninguna (any) after the verb:
• No he notado ninguna hinchazón en mi muñeca.
Or simply:
• No he notado hinchazón en mi muñeca.
Both are correct; including ninguna emphasizes the total absence of swelling.

Place derecha after muñeca:
• He notado hinchazón en mi muñeca derecha.
You could also say la muñeca derecha (“the right wrist”) once the wrist is already under discussion. In Spanish, directional adjectives follow the noun.