That would get the correct message across. I would say "The sunlight is harsh today" Or, "the sun is bright today" Or, "I'm going to get a sunburn out here! Better grab the sunscreen!"

The sun is shining so much that it is burning my skin.

'Sunshine' is normally used in positive contexts. I would say 'the sun is too strong'. These days, (possibly more in southern hemisphere countries) you could also say 'the UV index is too high'. ;) I don't think 'harsh' or 'bright' are the right words to use. They relate to vision, rather than burning. Check your spelling: sunshine, not suBshine. Also 'natural' rather than 'nature'.