Is it normal that at almost 6 weeks post op my left boob is very sore?

It's not uncommon to experience some asymmetry in healing after breast lift and augmentation surgery, especially around the 5- to 6-week mark. What you're describing—tenderness and soreness in one breast, especially when applying pressure, while the other feels numb—can happen and doesn’t automatically signal something serious, but there are a few things to consider:
What’s possibly normal:
• Uneven healing: One breast often heals slower or differently than the other.
• Nerve regeneration: Soreness can be related to nerve endings waking up, which may feel like burning, tingling, or sharp sensitivity.
• Implant settling: The muscles and tissue on one side may be tighter or more inflamed as the implant "drops and fluffs."
• Residual inflammation or scar tissue formation can cause tenderness, especially if you're using your arms or chest muscles more on that side.
What to watch out for:
Even without obvious signs of infection (fever, redness, warmth), keep an eye out for:
• Sudden increase in swelling or pain
• Visible asymmetry that seems new
• A firm, tight, or ball-like feel under the skin (could be a seroma or capsular contracture starting)
• Persistent pain that isn’t improving or is getting worse
Bottom line:
Mild tenderness at 5.5 weeks post-op can be within the range of normal, but because you're experiencing one-sided soreness that’s painful to touch or pressure, you should still check in with your surgeon to be safe. They may want to do a quick exam or imaging (like an ultrasound) just to rule out fluid buildup or early capsular contracture.

Hello dear!!
Thanks for your question and provided information.
You are still early on healing process. It is normal to be swollen, and you can expect to see your final results after 6 months. 
Please, be patient, but if the situation doesn't improve over time, I suggest you to follow up close with your plastic surgeon.
Hope this is helpful. Good luck :)