Hi and Welcome!
Never too late! There may be a period of adjustment that's rough, but you can weather that.
My son is 2.5 yrs. and he was a BIG hitter--from about 18-24 mos. It's hard! But, it is perfectly NORMAL. This is a tough time in their growth. I think a big part of this is that their minds are way beyond their language/coping skills--and that helped me a lot to remember. My son also has food allergies that contributed to this behavior. Finally, I had to get honest with myself and recognize MY urges to hit and lash out when I get really mad about something; to acknowledge how hard it is for ME (as an ADULT) oftentimes to NOT act on that. That gave me some perspective and empathy (and humility!).
Then I tried to teach him that hitting is not OK when you're frustrated, BUT there are other things one can do.
So here's what I did: He would hit. I would first try to focus on the above ("This is NOT personal. He is frustrated and doesn't know how to deal. Breathe!") BREATHE! (Breathing is important--it can change your mood. Don't underestimate simple breathing!)
I would try to stop it physically if need be (gently catching his arm or moving away) and tell him "No hitting. We do gentle touch," and gently stroke my face with his hand.
Sometimes we would offer him the option of hitting high five (explaining, "If you want to hit, you can do high five.").
Sometimes I would leave or do what you said: get in a place where he couldn't reach me--I never really found this to help him so much (in fact, it would generally escalate his behavior and frustration), but if it was at the point where I could feel myself losing control and fighting the urge to hit back, then it gave me a chance to breathe and regain some composure.
I used a lot of "projecting"--"You feel ANGRY don't you? You can say, 'I'M ANGRY!'" and I would stomp my foot and show him the sign for 'angry.' Or I would simply empathize, "I know you're frustrated b/c you want that toy. It's hard to share, isn't it?" Just try to give him some ways to verbalize or express with his body that he was pissed off that didn't involve hitting (and in your case biting).
I did this over and over and over and over and over again. I despaired that we would ever get past it (I'm sure there are plenty of posts in the Archives from me on this topic!). But after a while, it occurred to me: "Hey! When was the last time he freaked out on me? It's been a couple of days!" And it just started to be less of an issue.
And now he's 30 mos. and he is pretty much past it. Occasionally he will get upset and hit (and now he also yells "BAD!" Where he got that from is anybody's guess LOL--but I think yelling that is a pretty good way to nonviolently express his anger for right now), but I don't really have to focus on the correction part so much. He knows it's not the best choice, but he couldn't stop himself--no point in making him feel worse than he already does about it. I mostly just comfort him through the freak-out/hitting until he's done (usually he will dissolve into tears or ask to nurse), so I know it's more about him being out of whack emotionally/physically than anything else and we can work on that together. Oh, and now I encourage him to breathe, too! That really helps.
Hang in there--it will pass! The trick is to remain sane and help them through it the best you can. Punishment, to me, seems counterproductive b/c the behavior really is a symptom of something else.
Hope that helps! Hang in there and keep posting for advice--the mamas here have helped me improve my parenting enormously!