Sherlock and John have a very complex relationship. Which, besides to avoid the snide comments of Anderson and Donovan, is why they prefer to not be particularly public about it; people would never understand.
They don't hold hands.
They don't kiss.
They don't say "I love you", it isn't true.
Love does not and never will exist for them.
They don't let anything in their behavior allude to the fact that they are romantically involved.
However, back at the flat on Baker Street, you can find them together on the couch; Sherlock's head in the doctor's lap as they rest after a grueling case, watching whatever crap television just so happens to be on. John's hands will run through the detective's dark curls, massaging his fingers into his scalp as Sherlock thinks. The taller hums softly in appreciation, his hands clasped beneath his chin as he rummages through the files of his mind palace to delete unnecessary information.
It isn't a love, but a need for each other. A need to be held when the nightmares are particularly rough; a need to be reassured that world is wrong when they label you a 'freak' or 'mistake'; a need to know that you aren't alone in the world.
They keep each other sane.
Alive.
And that, is all that matters to them.