mfea just echoing what the others have said. I've done exactly what you did, the offering alternatives, the shouting, the being a bit rough, the dinner in the bath and the feeling shit shit shit about it later. And DS was about 15 months when it was at it's worst.
As someone else said, the fact that you feel rubbish about it is probably enough to ensure that you don't let it happen again, and proof that you care. (Actually, you probably will do it again, maybe not over food, and you'll feel just as rubbish). It gets easier. Do you remember the constant night feeding when he was newborn, and him not settling, and you being knackered and at your wit's end? how you thought it would never end and you wished someone would take DS away? Well, i do. And that passed and is a distant memory...so will this be.
So, we went back to easy baby food for a while (yes, purees). Put a time limit on it. Gave a main meal at lunch time and gave an early snacky tea (tired babies often don't eat).
Also, remember their appetite varies. in the first year they are growing so fast that they need loads of calories. by 15 months this has slowed, and if you DS (like mine) was not yet walking, he just didn't need the fuel. Sometimes they are under the weather, just enough to be off their food, not enough to really be ill.
Even at 15 months babies are starting to switch on to the consequences of their behaviour. Now is not the time to let them them to manipulate you, to learn that they have power over you where the high chair and food is concerned. DS is offered a small portion, he eats what he wants, then if he wants more he gets more. Sometimes he gets pudding before his main. But no choices for meals, no alternatives. As soon as he throws or spits food I take it away from him and offer no more. No "nice" snacks (if he is hungry between meals he gets cheese or fruit, just the fuel he needs).
DS at 20 months is way better, and has been for a couple of months. for the couple of months before he lived off bread and butter, blueberries, plain yoghurt, sausages. And baby cereal. A limited, but actually reasonably well balanced diet.