Essentially "whenever'' would be "sempre que", whereas "always" meaning would be "sempre". Just a rule of thumb, though.
In the sentence ''I can feel the sun whenever you're near." I would translate it into "toda vez que", so in this way it´s not advisable to insert "always".
Unless you rearrange the words in the sentence and perhaps adding other words as well (certainly beggining it with "always" and would risk to lose that original sense)
If you wish another word/expression, you could use each time/every time (every time rings more poetical to me, maybe because of the song that goes "every time you go...oh baby!).
Let´s wait for more comments.