Marsha's blog on CJ has visuals to help you figure out your texture Curl Junkie - Natural Hair Care for all types of Curly Hair!: My 2 cents on Protein/Texture/Porosity/Moisture Balance! :-)
It's not unusual for people with dry, curly hair to think it's coarse, when it's is fine (or medium.) Fine and porous hair usually likes/needs protein. It's unlikely that you would damage your hair with protein. The dry, frizzy, straw type look that feels soft could be overconditioning. In that case, you really do need protein.
The float test is notoriously poor. If you really have questions and can't figure it out, you can do the hair analysis on Live Curly Live Free - Hair Analysis
3a (Corkicelli), highlighted, fine, low porosity
modified CG, since April '07
CG since 3/11/08
HGs: Curly Kinks Satin Roots, Curlycue ReNew and Coil Jam; homemade FSG and okra gel; soap bars; DM MiraCurls Curling Gelly; UFD Curly Magic; Shescentit LIs; Sevi conditioners; Botanical Spirits Puree, CJ Repair Me