I'm day 14 BF and totally relate to the clothes being sore on nipples. I'm just sitting with my top unbuttoned and the window open a wee bit to try and 'air' them a bit 😂 I hope they toughen up soon! Yesterday I went to my mums and wore my silver healing nipple shields and breast pads in my bra. I'm leaking a few drops, not as much as you, so no advice there I'm afraid. I'm apply the lanishol nipple cream after every feed. Hopefully your supply/demand will figured itself out over the next few days and the leaking will be manageable with pads.
https://www.elvie.com/en-gb/shop/elvie-catch I’m still waiting for my Feb baby to arrive but when I was breastfeeding my first I used these and found them really useful.
I just use reusable breast pads in my bra. Eventually the leaking will slow down and stop after your supply has regulated. It did take my breasts a bit longer to stop leaking in the daytime with my first, I believe I was wearing breast pads for around 6 months but the leaking was a lot less. If you are suctioning the haakka onto the other breast you are effectively pumping and not just catching the letdown. Which is fine if this is what you want to do but just being aware that this will increase your supply and possibly make the leaking issue worse.
Medela sell really good nipple protectors for under clothes and milk catchers to put in your bra, you can get them on Amazon 😊