Is my Inner Tie Rod bad?

You need to visually verify where the movement is occuring. Jacking it up and checking for play is a great first step. What you need to do is actually see where the movement is coming from in order to know which parts need to be replaced. If there is deflection in the outer tie rod end, you'll be able to see the movement. There should be zero deflection between the tie rod and where it attaches to the steering knuckle of the vehicle. It is harder to tell on the inner tie rod on most vehicles, but you'll see where the inner goes through the bellows at the rack side. There may be movement there as well. You need to ensure you're not getting movement through the rack, though. If the steering wheel is locked, you shouldn't see much movement out of the rack, but there might be a bit there. Check both sides of the rack when moving one side. If the input going into one side is the same as the movement coming out the other, it means the inners are probably in good shape. If you're not seeing equal movement, you need to discover which side is bad, though it might be both sides.

Changing out tie rod ends usually isn't too hard. There is a special tool which makes it a lot easier to do this. Not that it is absolutely required to change the inner tie rod, it just makes it a TON easier on both pulling the old and installation of the new. You can find them online in places like Amazon. Just look for "inner tie rod tool set". You may be able to rent it or borrow it from major part store chains as well. The only other thing you'll need to worry about is an alignment. You can get it close by measuring both sides and making them the same length as the old.