as mac said, a dermatologist would be your best source., and if theyre at a loss, a tattoo artists should not override a skin specialist. mark and mac know their shit.. but just asking online, puts you in a position where you can get all sort of answers, even from a 14 yr old kid, acting like a know it all, and not giving a shit whether you fuck up your skin. here, no one is accountable as a professional that you can actually have proper access to, should something go wrong.
my opinion is.. you re being fuckin paranoid
I can hardly see the spots from the photo. I d either live with them, or get a tattoo because I want one, and not to cover anything. but if you walked in my shop, I would personally have no problem tattooing you.
1. cant know if the ink will show through or cover, but it s very easy to hide, just the same. if you decide to go ahead, I d suggest you do something that has a texture.. in those small areas. the colour will help hide them, but in the eventuality that you see a darker patch underneath, that would blend with the texture, as opposed to a clean, flat area. as an example, patchy feathers on a bird, or dotwork, or any thousand and one other things that would help the eye look collectively, rather that on the single spots. that way you d be fine both ways.
2. I don't know why your brown hasn't faded away, because I don't know what it is. but tattoo ink in that area would need double care and attention, for the simple reason that sweating, moving the arm back and forth causing friction wont help the healing. definitely not to do any workouts, jogging etc for the first week or two..
3. anyone can be allergic to ink. not sure if you were thinking of a coloured tattoo or in black / black and grey. your odds are way better with the last. I had once written to kuro sumi to ask as I had a client that was allergic to nickel. they texted me back and confirmed that it is all carbon / plant based, I would not be worried. you could check with the artists or the suppliers, or look up the ink, colour / brand's msds sheets up, if you have to. at one point, painful pleasures used to supply them, I think.
id say many inks are subject to more stringent control than the deodorants you used, unless it s cheap, china crap you re getting inked with. however, what happens if you disinfect your skin with a 70% alcohol wipe? since you also mentioned alcohol... tattoo inks contain a small amount of alcohol too. personally I don't think that s what the problem was, but it s good to keep it into consideration, as well.
what I say is not religion, just how I feel about your situation. however I hope the mentioned facts might help you come to a more informed decision.
merry fuckin ho ho