Toddler fussiness is so normal, but it normally kicks in around the time that they start toddling, and isn't so usual in a baby - on that basis I would try to get again to get a referral. Occupational therapists do look at 'sensory registration' (I'm not one, I just used to live with one and we chatted about it) and you mention that your little boy is also not keen on some textures when he's playing - it may be that he has high registration through touch. My toddler is also very fussy, but it started when he started to walk (which is typical) and I was also a very fussy eater as a child - normal toddler fussiness is largely hereditary, apparently.
One thing that might be worth trying: can you get him to play with food and textures as much as possible? Ie breadmaking, homemade playdough. Hand painting with paints. Squishing foods. Mud pies in the garden. It won't make him start tucking into other foods overnight, but increasing his acceptance of new sensations (touch and smell) could help in the long-term. Let him play with food as much as possible with no pressure for him to try it. Indulging in lots of messy play helps with all kinds of development.
Good luck - I think you're right to look at this properly now as if there are any issues, the earlier you get help, the better. If all's fine and it's just a phase, nothing lost.