I've been on biologic drugs for three years now (first Enbrel, now Humira) and they do have a tendency to give me all sorts of weird symptoms. Both have increased my histamine levels, so I'm often experiencing different sorts of allergic symptoms, e.g., rashes where my clothes rub against my skin, becoming allergic to foods I was previously able to eat, have weird tingling sensations in my lips at times and my asthma is decidedly unhappy, especially for the first several days following the shot (I, too, used to wake up wheezing at night, but don't anymore). I deal with the itching by using a good lotion, which has reduced it to a dull roar, stay away from certain foods and always carry my inhaler. These side effects are annoying, but the benefits of the drug are so significant for me that I'm willing to put up with the symptoms. I have to say, though, in the beginning of taking these drugs, I was constantly freaking out and went to my doctor many times to get things checked out.
However, I am not a doctor and don't want to assume that your symptoms are based in the same, relatively innocuous "I can live with it" reason as mine seem to be. What concerns me is the tingling and fullness of the lips and waking up gasping for breath several times a night - it's important that you don't ignore symptoms like this, due to the potential life threatening consequences if they should suddenly get worse. I recommend that you make an appointment to see your doctor as soon as possible to discuss what's going on - it's better to be safe.
If your symptoms do end up being of the kind that you just have to live with, there are things you can do to make life less annoying - find a good lotion (Aveeno is excellent), take Benadryl or another type of antihistamine when the itching gets bad, talk to your doctor about an inhaler, if you don't already have one and drink a lot of water (I've noticed the meds make my mouth really dry and that can cause wheezing if you occasionally snore).
Please let us know what the doctor says.