It's totally acceptable to apply to multiple companies and negotiate with multiple offers in hand; you could say to B, "Well, A is offering me ${FOO} a year and two week's vacation, but I'm really excited about the work at B; can you match their offer?" or something like that. But once you accept an offer, it's generally understood that you stop looking for a little while.

It's also totally acceptable to look for a new job while you're working; people get jobs they don't like, or jobs change, and people want something new.

But what it sounds like you've done here is applied at a company, gotten an offer, accepted it, and started looking for new offers immediately. That's unusual, and is definitely setting off some alarms for HR. You're worried that you won't like the job, but there's no way for you to know; you haven't started yet. You're jumping ship before you've even gotten on board; why would B extend an offer to you? How do they know that you won't accept an offer with them and then immediately start talking to C?

The thing to do is to not accept an offer you're not happy with; if one company gets back to you and you're still waiting to hear back from somebody else, it's okay to say "Can I have some time to think about your offer? I'm still waiting to hear back from some other companies, and I want to make sure I have a good understanding of my options before committing". And then you can say to the other companies, "I need a decision from you soon; I have an offer from A and I want to respond in a timely manner to them."

edit: Also what patio11 said; he is eminently qualified to give job-search advice, especially with regards to things like negotiations.