My daughter was the same way. She *hated* tummy time for the first four months and would just scream. I really worried that she was not going to develop upper body strength, that she would have a flat head, etc. I held her upright a lot because while it's different than tummy time, spending time upright also helps babies develop body strength and motor skills and it helps prevent flat head too.
Anyway, at 4 months, she learned to roll over from her back to her tummy and that was that. After that, she loved to be on her tummy. She was crawling at 6 months and walking at 10 months so in our case, her motor skills and strength developed just fine.