Hey Stefan, good to hear that you're back on track, but I'm sorry the biotin isn't being kind to you. I haven't heard of it inducing that type of effect before - I take 10mg/day and don't really notice anything at all. I don't think it's a big loss to your regimen though, it's an inexpensive and simple addition for most people that might generally improve biological conditions for hair growth, but it's definitely not finasteride or something you can't be successful without.
Stick with the minoxidil, you've been there before so I'm sure you're not expecting anything after 12 days. If you are looking for something mild to replace the biotin that will help speed up hair growth, I would look at taking MSM - methylsufonylmethane. It's a sulfur-rich supplement that some people take to improve joint health (similar to glucosamine and chondroitin supplements) but has some other beneficial functions as well, one of which is pretty well known to be an increase in hair growth rate. If you take a look at the long-hair communities and ethnic hair care communities ('long hair care forum', longhaircommunity.com, my favorite: black hair media forums) MSM is the supplement of choice. It seems to be well-known amongst long-hair enthusiasts that MSM makes it grow out faster. Whether this is good or bad for those of us with male pattern baldness is not so clear - it may advance more hairs into the anagen phase giving you a fuller head of terminal hairs, or I suppose it's possible that it increases the rate of turnover such that male pattern baldness's effects are accelerated. I tend to favor the first hypothesis - I started taking 3g (yes, 3 grams!) of MSM a day in the first few months of my treatment plan (1.5g in morning, 1.5g at night) and have had really good results, to the point that I continue taking it to this day. Of course credit primarily goes to the finasteride, minoxidil, keto, and spironolactone, but the little things like MSM and biotin deserve mention too, especially at a cost of just ~$10 per month. Plus it's nice to have a treatment for which you'd actually expect beneficial side effects, as is the case with MSM and its therapeutic effects on connective tissue and elsewhere in the body. In fact, in all my research the only things I've found to have an unequivocally positive (or at least non-negative) impact on health are omega-3 FAs and MSM. I've come across a number of studies on supplemental MSM intake, I don't recall any noting any adverse effects. From my own experience, I would say - subjectively, but with some confidence - that it does make your hair grow out faster. When you're starting (or restarting, as in your case) treatment with finasteride or minoxidil or whatever, I would conjecture that the increased growth rate works to your benefit in generating results more rapidly. [I suppose the converse would be that if you're faced with a fixed number of hair cycles over a lifetime you would also reach NW7 more quickly, but I don't think such a model of fixed-lifetime-growth-cycles has been supported). I take NOW Foods MSM (EDIT, see below) in 1.5g tablets by the way (they're big and chalky pills, but inexpensive and effective. Liquid versions are also available). [EDIT: My mistake - I actually take Drs. Best MSM in 1.5g tablets, as this brand now uses the highly preferred 'OptiMSM' form of MSM made by Bergstrom Nutrition in the US. An alternative form is Lignisul MSM, made by Fine Neutraceuticals, which is the form Drs. Best used to include, although the non-scientific anecdotes I came across tended to favor OptiMSM.]
Good luck, stick with the minoxidil and don't over-do the tretinoin.