I'm guessing as others have said, you must have a bug in your game. I hope you can get this resolved soon. Anyway, I can help you with getting plants for the Science career. Although, that must be another bug in your game too because they supposedly fixed it in a recent patch. Plants grow at the lab and at festivals in my game now. Is your game fully updated?
Anyway, to get plants you need to make serums since you can't grow much of anything in your home garden, just click on the plant pots in the lab (or at home if you have any) and order seed packets for the type of plant you need. You might have to order more than one, but it's a workaround.
Sims can also get plants and seed packets by using the 'purchase gifts' option on their cell phones. The individual plants will cost 'much' more than getting them from the plant pots though, but the seed packets still cost the same. Just an idea, I hope it helps!
One last thing, I'm sure you probably have by now, but just wanted to make sure it's been tried as suggested. Have you repaired your game? I always do that after updating with a patch or after loading a new game pack. I'd also clear out your cache files and delete the localthumbnail package file too. :)