I use my thumb since I find normal picks too inaccurate for anything but strumming. Since I've built up a lot of muscle memory for my thumb, would a thumbpick be a smart choice for not wanting a sore thumb?
Are you just using your thumb? If so, if you're starting out, I remember being in a very similar position and I'd encourage you to persevere with picks. Fingerpicking as such is a useful technique, but playing with your thumb is going to give you real trouble playing things normally played on a flatpick, especially fast things. Possibly look into something like a Dunlop Jazz III - a small pick with a point that stays close to your thumb. I know of one guy (Chris Zoupa) who uses his thumbnail as a pick, but that requires having a long thumbnail and taking very good care of it.

To answer your question, a thumbpick requires a different technique again. Typically they stick out quite far from your thumb and are quite awkward until you get used to them. They also have a pretty different sound from a thumb and, because of their design, are likewise generally not ideal for things played using flatpicks. As far as soreness is concerned, the answer is usually to grin and bear it, really. Everyone gets that when they're not used to something (I certainly do when I haven't been fingerpicking enough and then I play something with a lot of hard fingerpicking), and you can only really get past it by building up callouses. Note that the same does not apply to joint pain, which should be treated with a great deal of respect as damaging joints is substantially harder to come back from than raw skin.
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Are you new to this technique? If so, you'll just get a callus there and the pain will stop. Some really great electric players used only fingers. Mark Knopfler, Chet Atkins, Jerry Reed... Wes Montgomery used just the side of this thumb and was good enough to do down and upstrokes.

And there's no such thing as pick accuracy, only picking accuracy - it's mostly a matter of technique. You may find it easier to be precise with a smaller pick, such as the Jazz III.

Unless you actually want to pursue fingerstyle, your best solution is probably to work on picking technique so you don't have to use you thumb in the first place. There's nothing wrong with fingerstyle, but I wouldn't default to it just because of a simple technical challenge.