Did anyone feel sick after eating oysters?
Yes, as well as other seafood from time to time. That's why we very rarely eat seafood in a restaurant, don't buy Asian seafood at all, buy only farmed oysters, clams and mussels from reputable North American places, and only buy wild caught shrimp, fish, etc. otherwise. But, we are lucky because we live in a place where we can always get fresh wild caught seafood.
Not sure how it is in England, but in the States seafood has to be labeled with point of origin and date caught. The store has to keep a log of that and when it came in, so I always ask. We also try to go on delivery days.
The reason we stopped eating seafood in restaurants was because I ordered a clam pasta at a mid-level national chain with the initials MG. Quite a few of my clams were served still closed, so I sent it back. The clams were brought back open, but upon inspection, there were pieces of shell that had broken off when they forced them open. Needless to say, dish got sent back and I filled up on bread and picked at DH's plate. Didn't want to order something else there. The other time, and the one that clinched the no eating seafood in restaurants rule was at a fine dining establishment with a chef we knew. I had ordered a multi-seafood pasta dish and it was great. The chef came out after dinner service had slowed down and sat down to chit-chat for a few. After complimenting him on the meal, told him about the MG incident. He came back with something along the lines of "well, I'll just open them before they go out." Being kind of flabbergasted, either I or DH said something about the rule that if they don't open you toss them. He came back with "they are nearly always alright so I serve them." That did it for me. We did continue to go to that restaurant but didn't order seafood there again.
As to levothyroxine and iodine allergy, I've been on the med for the better part of my life and I do have an allergy to iodine. None of my doctors have ever told me to avoid seafood. Only twice have I had a reaction to seafood, once in Italy where I was eating fresh fried anchovies and I swear I could taste the iodine in them, but I ate them anyway (stupid, but I was in my early 20's on vacation in Europe for the first time, what can you say) and I ended up with a blinding migraine. The second time was at a local chain restaurant and it was some kind of crab. No iodine taste but I got hit again with a fortunately quick this time blinding migraine. Course that time could have also been because I was having dinner with my mother and she was being her usual "loving"
self.