flump...thank you for that helpful post.
As far as the tinnitus is concerned it may well be due to the onset of the ageing process and of course Methotraxate may well have instigated the onset of your tinnitus and if it came on before taking the drug, then the MTX may well make it worse.
It would seem that you are dealing with the tinnitus, but the pulse is a new symptom. You do not say whether the pulsation is in one ear or in both, but in my opinion this is due to the flow of a blood vessel in the middle ear and is of no threat to life or limb.
Personally I would not got to see you GP at this juncture.....monitor the pulsation for about six weeks and then, if there is no improvement, seek medical help.