Could a Loxodon in full plate armor with tower shield in one hand, wield a greatsword with the other hand and their trunk?
Nope, not by RAW.
From Guildmasters' Guide to Ravnica (p18), in the Loxodon's traits:
Trunk. ... Your trunk can't wield weapons or shields or do anything that requires manual precision.
Unless of course you have a generous DM who is willing to bend the rules, then that's their call.