So there are going to be a fair few different 1/2 marathon plans out there but I think you're weekly mileage seems OK. It looks like you're doing a plan for an 'improving time' runner (i.e. not just a 'casual get round' type plan) .. which is fine for a beginner, if that's what you want and your body is dealing with it OK
Most semi-serious half marathon plans (not elite - just for people chasing better times) will list 5 or 6 runs per week .. and not mention cross training so there's nothing too wrong with just running. But having said that a cross-training session helps the body and reduces the risk of injury from overtraining (more of an issue when you're starting out) - I think you can add swimming and cross and still do long runs no probs. It's only when you start chasing really fast times that you need 6 runs or so per week. Again you need to balance your goals - fast times / weight loss / no injury!
With your weekly runs - rather than go 'long' on all .. most plans will make you do a speed session (fast shorter intervals), a tempo session (longer intervals) and a long run .. and then add some recovery runs around that. So it's not all about adding the miles .... other stuff will make you faster and give you different workout.
All this said and done.. you're not doing anything too wrong and only you can say if its over the top for a newbie! You're doing great mileage for someone who's only been running since March .. so listen yo your body, stay injury free and enjoy