An amplified splitter might help, but I think the losses in your system are due to something else. So before you spend any money on an amplified splitter there's a couple of trouble-shoot tips to try.
1) Remove the existing Y splitter and connect the aerial leads together for a direct connection to your room. [Note: this is only a temporary test just to check signal quality]
2) Do a factory reset and then retune on the TV
Doing the above will show you whether there's enough signal from the aerial to give you the missing channels. It also confirms that the TV is scanning the entire tuner frequency range.
If you get the missing channels then the next step is to reintroduce the splitter. If the TV loses that channels again then you know that the splitter is tipping the balance. That indicates a very marginal signal.
Causes of a marginal signal:
If your aerial was properly installed by an engineer who knows what he's doing then there'll be plenty of signal from it. Splitters always introduce a loss. Splitting two ways means half the signal on each leg, but the splitter itself takes some power too. With the plastic splitters you'll actually get a lot of loss; so there's only 25% of the original signal on each output leg. That's still okay though. With a decent aerial you could split again and still have enough signal for decent reception.
If the lounge TV is still good despite some fairly heft signal loss from the splitter then the obvious question is "
How come so much loss to your TV?"
Presuming you have spliced in to the main aerial cable, and it's decent stuff with copper braid over copper foil for shielding, and also you used the splitter the correct way (it should be like an upside-down Y; the tail of the Y pointing towards the aerial), then the answer is partly the splitter but mostly the extension cable to your TV. If you bought one of those DIY TV extension kits that comes with cable, plugs, splitter and clips then that's the culpret. The cable is cheap crap. It loses a tonne of signal compared to decent TV/Satellite coax cable (WF100).
If you put a powered splitter in then it will do two things. The first is that it compensates for its own presence. i.e. what you lose by splitting then you gain back from amplification. The second thing though is it introduces noise. This is on both outputs; yours and the lounge TV. So the risk is that you still end up with no SD channels in your room, and the lounge TV gets messed up too. Passive splitters don't introduce noise. If there's enough signal in the first place then a passive splitter is always better than an amplified splitter.
In your situation I'd buy a metal-bodied passive splitter with low insertion loss (
LINK) and some WF100 coax (
LINK) and get your system working properly.
