First of all, I think you need to look at strength differently.
What if I asked you which is more important on a car, the tires or the engine?
What would you say?
See my point?
It's not only all good, but it's really all essential if you are talking about defending yourself in a street confrontation. You need strength, speed, skill the whole package! How many skinny, weak 130 pound guys start street fights?
Answer: Not many.
The street thug who attacks you is probably going to be bigger than you. Did you ever notice that as a rule big strong guys don't usually get singled out for being bullied?
Most bullys really don't want a challenge. Some street thugs do...but most would rather have an easy night, it's just human nature.
Keep lifting and trying to up your numbers in the big lifts. Especially the Deadlift, Squat and the Overhead Press. And there are others.
In the mean time understand that if you are afraid to get hit in the face you are probably not going to be able to defend yourself very well against a tough guy. That means you need to go to a place that allows you to take a shot at least now and then , if not semi-regularly.
That's why I like Boxing. When you are boxing someone is really trying to punch you in the face and that's a good thing. Okay...it doesn't sound like a good thing huh?
But, trust me it's a good thing if you are really trying to prepare yourself for a street confrontation.
I also like any grappling art as most confrontations have some sort of grappling component. Of course the Hollywood version of a street fight may not have it...but then again that's all bull. Just like the myth of the indestructable Black Belt is a lot of hooey.
If you're smart you will skip ALL of the traditional martial arts schools. They turn out Black Belts the way McDonalds turns out hamburgers. And quite honestly the quality is just about as good!
Sure there are some good ma schools out there, but it's much easier and better in the long run to do the boxing and grappling thing. Especially in light of the fact that you said you are not interested in kicking. You can get very very lethal with just your two fists and some very good grappling ability.