Do I have to take prednisone for an allergic reaction or will I be fine?

So I'm pretty sure I got bit by a spider on my arm. I have no idea what it was but almost the whole back of my arm is swollen, itchy, and warm to the touch. It's not painful, the itch is just really uncomfortable.

The doctor prescribed me antibiotics just in case it is a spider bite and prednisone. The problem is I'm already a pretty anxious person, especially when it comes to taking certain medications with mental side effects. I've had way too many bad experiences with medications inducing panic attacks. I've heard prednisone can cause panic attacks, insomnia, and even depressive episodes. I'm really not trying to be miserable and feeling insane for the next week so do I really have to take it??? Or will I be fine just taking Benadryl and the antibiotics??