Yes, it is a comma splice. The word "however" is a conjunctive adverb. It cannot be used as a coordinating conjunction to connect two independent clauses with just a comma. It needs a semicolon or period before it.
Both of your others are correct, but they have slightly different meanings.
Thinking of you (or something) is a short-lived, spontaneous event. Thinking about you (or something) is a longer, more purposeful happening.