Hydrocortisone or Betnovate (both steroidal creams/ointments) will clear that up in no time at all. However, you need to let the medication do its job and that means taking a break from playing. If all goes well it may be less than a week. If you're unlucky, two weeks. If you don't let it heal, especially doing 5 hours every day, it simply never will.
And once you're healed, you can then find the cause.
Are you biting?
Are you playing while rarely taking the mouthpiece out of your mouth so the reed and lip is constantly wet, causing chapping?
Is the reed too rough?
Are you playing for too long?
Is your emboucher too tense?
Are you taking too much lip over your bottom teeth?
I also suffer from sore/damaged bottom lip from time to time, too. Thankfully it's become less frequent but it still happens. Oddly enough, when I first started, I had irritation in exactly the same place as you.
For me the solutions were to not let the reed become too wet when practising for long periods of time, relax my emboucher (otherwise you're basically grinding your lip into the reed) and play with a much more 'lip out' technique. I always polish my reeds on paper, which helps a lot and I always address any soreness before it becomes a problem. Usually this is little more than lip balm and a day or two off from playing.
When I saw your pictures, I saw chapping that hadn't been allowed to heal. First the skin becomes dry. If it's not addressed immediately, that dry skin starts to itch. Once the itching starts the skins becomes red and inflamed. At this point there is no other option than to stop irritating it. The weeping you describe is the skin trying to heal.
Imagine you have an itch on your finger caused by a piece of grass tickling the skin. Rather than remove the grass you scratch the itch. And then continually scratch that itch for the next two months. You can imagine what the skin on your finger will look like. That's what you're doing with your lip. The reed is constantly rubbing the already sore and delicate skin.
When you started your BMus, did your practise regime suddenly jump from an hour or two every day to five? That's a big jump and would explain the sore lip. Continuing to play for five hours a day explains why it's not had chance to heal.
Did you go from playing relatively quietly in your practise room to regularly playing at volume with other musicians? This would also explain how the lip initially became sore. And, again, if you continued to play at volume without allowing the healing process to take its course, why it's still a problem now.
Have you changed instrument or had it checked for leaks? These may sound like strange questions but I recently changed instrument and found my new sax allowed me to radically relax my emboucher. My old tenor had no leaks yet when I went back to it I found I had to put a lot more effort into playing it. My lip is a much happier appendage now thanks purely to my new horn.