Not necessarily. Not only does it depend on what kind of abx, it's highly unlikely that you were given strong enough abx to treat the Lyme infection, so you might not have noticed anything at all simply because the wrong abx were used or they weren't strong enough. Many people don't feel a thing from 200 mgs of Doxy daily - even though that's is one of the most effective treatments in the first few weeks of infection. The dose to be effective is 400 mgs a day, and many people feel the effects of that when they have Lyme, although at times, 600 mgs a day is needed.
The Lyme disease bacteria is constantly changing it's outer surface proteins to keep our immune systems from 'discovering' them and producing those antibodies, as well as inhibiting (lowering) our immune function. Blood testing won't likely show much for you because it's been so long, so do be sure to get the Western Blot so that if you have any band show up as positive or IND it will be seen. If you post those results here, we can help you interpret the results, or you can go here to find out on your own what the results are, and to find supporting Pubmed articles showing what the bands represent.:
www.oocities.org/hotsprings/oasis/6455/western-blot.txt The fact that you have had Bell's Palsy and have other Lyme symptoms should get you started into treatments to see if you have a reaction to a good treatment plan. If you begin to feel better or if you herx, then you know you have Lyme.
My own healing story started out with a 40 year old Lyme infection, so it doesn't go away on it's own once it starts causing symptoms.