T1/T2 are joined (effectively the same building now) but with separate security for the UK domestic vs. international parts. Luckily for you the international part of T1 is nicer and connected to T2 (the usual LHR long walk). I've never used the IB lounge but the other lounges (other than BA) are abysmal and I doubt any have showers. All of the BA lounges do have showers (usually with no waiting at T1). You can walk from T3 to T1/T2, takes about 10 minutes at a brisk pace. As for getting to the BA lounge, there isn't one in T2 so you follow the signs to T1 if you are using the FCC. Just head for the BA First lounge (only in the international part of T1, which you should be able to access, but BA has been known to turn non-BA pax away without recourse -- probably best to use the AA arrivals lounge).