I don't meet the experience level you are asking for help from, but given the lack of input so far I'll offer something.
I have never read anything that would lead me to believe there is any problem with taking BB when suffering from the conditions you mention. That said, BB tends to give me some fatigue and I'd "guess" that can't be helpful if one is having a panic attack..but it may not be a key factor.
The dose levels you mention are very low, to the extent that I understand..I take Metoprolol at the 100 mg level to control my AFib stimulated high HR, so I assume as your stated levels are much lower you are indeed taking lower BB levels.
My experience says you need to get your tachycardia under better control, well below 100 at rest. Mine runs in the high 70s to 90 when at rest. Again, AFib is the driver, so it varies.
I also have panic attacks and asthma and i take xanax and advaire for them I also have pvc's pac's and svt and i take 120 mg of inderal and 120 mg of verapamil and have noticed no problems to speak of. The inderal is a beta blocker and the verapamil is a calcium channel blocker I really haven't noticed either making my asthma worse. I guess if you are worried talk to your doctor and pharmacists and see what they recommend.
The problem with SSRIs (like Zoloft) and Beta blockers is one (I think the SSRI) prevents elimination of the other (beta blocker), creating a situation where you are actually getting a much higher dose than the doctor intended, potentially elevating concentrations to toxic levels.
And yes, BBs and asthma are supposed to be a bad mix. Here's a relevant article: http://www.medscape.com/viewarticle/568773
I found an article relevant to the SSRI/ beta blocker question: http://www.drugs.com/drug-interactions/propranolol_d00032_citalopram_d04332.html
If the link gets truncated (too long for the screen), email me at jeffsskippyheart[at]yahoo[dot]com and I can send you the full link.
It does look like from that article that you have some options, but that you have to be careful to monitor your vitals for awhile to make sure BB's aren't accumulating in your system.
You should talk with your doctor about taking advair for your asthma. Did you know that it has a black box warning concerning heart arrhythmias? Advair contains two medicines: flovent and serevent. Flovent is a corticosteroid for inflammation and serevent is a long acting bronchodialator. Serevent is the drug that can interfere with heart rhythm.
When I started having symptoms in April, I stopped using Advair and now I only use Flovent. When I saw my pulmonologist I told him that I was only taking flovent (he had given me a prescription for both to use when my asthma got really bad.) He agreed with my decision.
Regarding my symptoms, I am waiting to see my cardiologist on Thursday so he can tell me how my 30 day event monitor went.