Menopausal anxiety is usually caused by a reduction in oestrogen levels.
You could consider taking soya isoflavones to gently support your oestrogen.
This would be OK with your anti-depressant. One interesting fact to note is that antidepressants can cause changes in blood sugar behaviour, and if your blood sugar is a bit wobbly you'll feel more panicky and light headed - a vicious circle!
So it would be important to focus on eating regularly - have something, however small, every 3-4 hours, e.g. a banana or some dried fruit or nuts, chewing them well to improve the absorption of the nutrients they contain.
Also, keep your water intake up (but don't drink with food - leave at least 20 minutes between food and drink), as dehydration makes you feel way more panicky and gives you palpitations. Avoid caffeine if you can, as this can trigger panic attacks too, as can very sugary foods.
To help yourself further, start practising simple breathing exercises several times daily. Just something as easy as counting to 3 whilst you breathe in and again to 3 as you breathe out will be very helpful - you may be surprised at how good this is at averting panicky feelings.
Get some gentle outdoor exercise every day if you can - just 10-20 minutes gentle walking makes you feel heaps better, as hormones circulate in the bloodstream so keeping active is a good fix.
Check your diet for wholegrains, dried fruit, nuts, seeds and green vegetables, as these are sources of magnesium and that is very stabilising for your adrenal glands.
You could take an extra magnesium supplement too (e.g. Salus Haus liquid magnesium), and there is some in the isoflavone supplement I've mentioned. Herbs such as Passiflora and Avena sativa can be extremely calming too.
So don't worry, there are plenty of ways of tackling this and making sure you have a better ride through the menopause.
Prioritise your relaxation time - this is the best excuse you'll ever have to do things you like and look after yourself well!
The problem with going on HRT is that at some point you have to stop taking it and the withdrawal symptoms can sometimes be worse than the original symptoms so if you can avoid it all the better!