OK, my tip would be to go back to the GP and ask for Lansoprazole FasTabs. These have two advantages over omeprazole MUPS. First, they dissolve properly in water; second, they taste of strawberry so more acceptable taste. It's the same class of med as omeprazole.
Whichever drug you end up with, I have found the best way to do it is to get a small receptacle, like an avent bottle top, put the pill in to say 10 ml of cooled boiled water, prod it a bit until it dissolves but don't crush. Then, swirl around in the bottle lid until the granules (the active bits) settles in a circle in the middle. Then, using a 5 ml syringe (boots do them) or neurofen syringe as PP has mentioned, suck up whatever proportion of the granules is appropriate -e.g, if your baby is taking 7.5 mls of lansoprazole, suck up approx half the granules (each tab is 15 mg). Then, gently squirt in to the cheek - you need to agitate the syringe and will probably need to keep flushing it out with some boiled water. If bits get stuck, remove the plunger from the syringe and hook them out with a clean finger, then wipe in your baby's cheek. Again, wash it down with some water.
It's a complete palaver, but omeprazole/ lansoprazole are more effective than zantac for serious reflux.
Your doctor might have failed to mention that omeprazole is best given with something a little acidic - e.g., juice BUT it should land in an empty tummy, or as empty as possible.
Good luck, it's a bind, but you'll find your own way of administering it as the days go on.