Coughing and hiccuping baby plus sore right boob

Emily

My little girl is one week old and I’ve been noticing for the past day or two that she sometimes stops feeding to cough for a second or two. I pull my nipple out from her mouth and sit her up and pat her back while she coughs for a second or two and then she seems fine. Is this from an oversupply of milk? She also gets hiccups pretty much daily, sometimes multiple times a day. Wondering if that’s a sign of oversupply as well or maybe she’s just sucking air. She’s latching really well now though so maybe not? I also have been experiencing pain in my right boob. The whole right side of it is tender to the touch, even after she feeds from it. If it’s a clogged milk duct what can I do to help unclog it? I know warm compresses and to let her feed from that boob first before switching her to the other one but any other suggestions?