Before getting hand-scoring for your test, you should definitely consider doing the Test Information Release, which is available for April, June, and December official ACT test dates at national test centers. TIR costs $20 and gets you a copy of the multiple choice questions, a list of your answers, the answer key, and (if you took ACT Plus Writing) a copy of the essay prompt and essay scoring guidelines along with your essay scores.
This'll give you a chance to go over your answers, the answer key, and the questions. You'll either be able to clear up your confusion (for instance, you might find that some of the answers you were positive you'd answered correctly you got incorrect) or be able to verify that something went wrong and then order Hand-Scoring for a fee ($45 for multiple choice, $35 for the essay section).
If you didn't take the ACT in December, April, or June, you might want to consider doing regular Hand-Scoring anyway (since your practice test English scores and your actual English score were >5 points apart). Just make sure that whatever you decide, you do it quickly - you can only order hand-scoring and Test Information Release within three months of your test date!