My Dilantin medication is cause swelling in my gums. Are there any home remedies to alleviate the swelling?

Somewhat. It depends how severe. Good dental hygiene is key. Frequent brushing and dental floss, multiple times each day will help. If it is severe, then you will need the help of a dentist, to surgically decrease the increased size of the gums. If untreated, this could lead to tooth loss. If severe, alternate anti-seizure medications should be considered.
Probably not. Gingival hyperplasia is a listed side effect of dilantin. I would think that the only way out of this is if you can be switched to another class of antiepileptic that does not have this side effect. Of course such a switch depends on your type of seizure and if there is a suitable alternative.