Try to get the luggage checked through all the way. Last week I flew FCO-LHR on BA and LHR-LAX on AA. They were booked separately, however at checkin in Rome the BA agent asked if I wanted my bags checked all the way to LAX. I didn't trust them to do it so I declined seeing as I had 5 hours to connect at Heathrow.

So I connected T1 to T3. We landed at 11:30 am and just went landside through immigration and picked up my luggage then walked to Terminal 3. I was checked in with AA and on my way through security at 12:15 pm.

It's doable, but it depends on the time of day. 90 minutes seems way short though if you have to recheck your bags. Plus the immigration lines at T3 at peak times are ridiculous and it usually takes AA quite sometime to get the luggage coming off the plane.

If you can get your bags checked all the way through you can probably make it.