No, however shouldn"t always start a sentence, but we can put it at any place of a sentence.It can be used as a conjunctive adverb and preceded by a semicolon and followed by a comma.
EX:
Diana and Tom love eating lunch outdoors. However, they do not love the flying insects.
However can also used in the Middle of a Compound Sentence
EX:
Winter is a lovely season. Spring, however, is still my favorite season of all."