Shifting Issue on Lower Strings

Hi, I'm a conservatory student in the Netherlands and I've recently switched from electric to upright and I am starting to really appreciate and devote myself to this instrument. I was hoping some of you guys in this forum here might help me:
I had the problem for a long time that shifting on the E and occasionally the A string is very hard to do and causes a lot of friction. This tenses up my hand which makes my whole technique fall apart especially when I play a F# and B Scale where you have to shift from half to first position with your index. This is extremely frustrating as I can play and shift fluidly and relaxed with most other scales and appreggios, but whenever it requires said shift I tense up and my left hand tires. My teacher keeps saying that it is a matter of developing the necessary muscles but I don't really see how that helps reduce the friction between my fingerpads and the string, and I've been practicing for hours weekdays for the past half year (specifically said scales and Appreggios), to the point that I have permanent grooves and some pain on my fingertips that seem to bite through my callouses on my left hand. This issue still remains a problem in my technique and hasn't improved since.
Btw I'm not talking about friction between thumb (which I try to keep as relaxed as possible but tenses up once I fail to execute the shift cleanly) and the back of the neck but between my fingertip and the string itself. The double basses in the conservatory have pretty low string height (compared to the one at the local venue) so I don't think it's that. Another thing is that my hands are quite dry, to the point that I need to use moisturiser so maybe that somehow prevents me from shifting properly? Or is it as my teacher says and I just have to bear through it until my hands get used to the shift?

Thanks in advance, I know this is a very specific question/problem but I hope some of you guys know what I mean and can help me with this problem...

 

Thanks for the reply! So you’re saying you’re lifting, for example, your index finger while shifting from a F (Estring) to F# or G? Because my teacher taught me that I have to sustain the note and not have any breaks in between when going from one note to another, which means I have to press down while shifting from F to F#, right?